Nameless Narrative

Who needs names? Plenty of stories, jokes, and even myths eschew them entirely in a Nameless Narrative. If a character is "named", it's more than likely to be as their role in the story or the job they have. Sometimes, the "name" might be a unique and prominent feature to them that serves as a reminder of their basic description, such as "the one eyed man", or "the silver haired maiden".

Stylistically, it's very economical in terms of prose and narrator memory (many Nameless Narratives come from the Oral Tradition) and at times elegant, distilling a character's essence down to their archetype.

The Nameless Narrative also works hand in hand with The Law of Conservation of Detail and Nominal Importance, allowing for a small named central cast and many nameless extras. This is usually because it's simply easier to remember the background characters this way than to give them all sprawling motivations and backstories.

Compare Everyone Calls Him "Barkeep", No Name Given.

Anime & Manga

 * In Maoyuu Maou Yuusha the characters are referred to even by each other with by their titles and positions, such as hero, female knight, demon queen, lone winter king…

Comics

 * Even though we already know their names (or perhaps because of it), Batman and Joker are never referred to as such in The Killing Joke. Even the newspaper clippings only call them "Disfigured Homicidal Maniac" and "Bat-garbed Vigilante." This works well with one of the themes of the book, which is that the two of them have gotten so intimate with each other (no, not in that way--maybe) that there's no need for names.

Fairy Tales

 * Most have only one or two named characters, but frequently, you have none.
 * Grimms' "Bearskin" -- unless you regard "The Devil" as a proper name
 * "East of the Sun West of The Moon": The heroine is "the girl"; the hero is "the White Bear," and later, "the Prince".
 * Grimms' "The Girl Without Hands"
 * "Diamonds and Toads"
 * Grimms' "The Goose Girl"
 * Grimms' "The Twelve Dancing Princesses"
 * "The Golden Blackbird"
 * "The Old Witch"
 * Grimms' "The Singing, Springing Lark"
 * "The Small-Toothed Dog": The heroine tells the dog its name is "Sweet as a Honeycomb" when she's trying to coax it, but there are no other names.
 * "The Blue Mountains"
 * Technically, the name "Snow White" is just a description of the fairy tale's heroine.
 * Similarly, "Red Riding Hood", although many evolutions of the story have that become her nickname.
 * In the original story, the princess is just "Sleeping Beauty".

Film

 * In the early days of America's Silent Movie industry, many audiences were made up of immigrants who could speak little if any English. Many films that weren't adapted from other media had characters named The Boy, The Girl, The Mother, etc. This allowed viewers to more easily identify with these characters. Even in the later years of the silent era, some filmmakers would occasionally use this trope, especially if they were trying to promote an aura of universality in the story:
 * In F.W. Murnau's classic silent film Sunrise, the main characters are called the Man, the Wife, and the Woman From The City.
 * Cecil B. DeMille often did this in his films.
 * Ditto D.W. Griffith.
 * Marilyn Monroe often played characters simply called "The Girl".
 * Throughout Zombieland, the only person referred to by name is - everyone else is referred to by their home or destination. The girls' names are revealed at the end (though one is hard to catch), but the men never really have names.
 * In Christopher Nolan's Following, only one character is referred by a name, and that might be just a pseudonym.
 * In Your Friends And Neighbors, none of the characters are referred to by name. In the credits, they're given placeholder rhyming names such as Cheri, Jerry and Barry.
 * Only three characters get names in Curse of the Zodiac, and one of those names is only revealed in text just before the credits, which only list the actors, no character names or titles.
 * In Exam, the main characters insist that they only go by pseudonyms based on their physical appearances (save for one character): White, Black, Blonde, Brown, Brunette, Dark, Deaf, and Chinese Woman. The other two characters are the Guard and the Invigilator.
 * Indiana Jones and the Last Crusade. In the flashback opening, the looters who steal the Cross of Coronado are credited simply as "Fedora" and "Panama Hat" (The former is addressed as Garth by one of his cronies).

Literature

 * In the Canterbury Tales, almost all the pilgims are unnamed and are identified solely by their occupation. The only pilgrims explicitly named in the work are the Prioress (Madame Eglantine), the Cook (Roger), the Reeve (Oswald), the Friar (Hubert), the Wife of Bath (Alisoun), and the Host (Harry Bailey).
 * In H. G. Wells' The Time Machine, the Time Traveller and most of the people to whom he's relating his story are just identified by their role, such as the Doctor and the Writer.
 * The characters in José Saramago's Blindness are referred to by their roles or, ironically, psychical descriptions (given the fact all of them are attack by blindness).
 * Saramago does this frequently, in whole or in part, for example in Seeing, Death with Interruptions, and (ironically) All the Names.
 * The kid and his grandmother in Roald Dahl's The Witches.
 * Hard-Boiled Wonderland and the End of the World.
 * Everybody in The Tale of Genji is referred to by their titles.
 * The father in The Swiss Family Robinson (who is the narrator) is never referred to by name.
 * A Nameless Witch
 * Aimee by Mary Beth Miller. The narrator reveals everyone else's names, but her name is not revealed until the last few pages.  The main reason was that the narrator could not detach herself from her dead friend Aimee, who she was accused of murdering.
 * The narrator in Isaac Asimov's short story "Robot Visions" doesn't give his name and doesn't differentiate between the scientists working on a Time Travel project, saying that these things aren't necessary for his account.
 * Surfacing by Margaret Atwood has a nameless narrator.
 * Phantastes by George McDonald has very few names revealed
 * Jessica Day George's "Sun and Moon, Ice and Snow" (based on "East of the Sun West of The Moon") has the main character known only as 'Pika' (girl) or 'Lass' because her mother refused to name another girl, and only a mother can name the daughters. She's given a name by the white reindeer to protect her from trolls, but it isn't until late in the story that she reveals it. The prince in the story also remains nameless for the majority of the story, but mostly because he never did get a chance to tell the Lass his name.
 * Stephen King's short story The Man Who Loved Flowers (published in the collection Night Shift).
 * Cormac McCarthy's novel The Road, and its film adaptation.
 * E.L. Doctorow's Ragtime starts out only mentioning the names of real people who figure into the plot while the fictional protagonists remain nameless, so "Mother" meets Harry Houdini. About a third of the way through, the pattern is subverted when the fictional Coalhouse Walker Jr. shows up.
 * There Is a Happy Land by Keith Waterhouse
 * Edgar Allan Poe's The Tell-tale Heart, which makes the old man's murderer's identity and relation to him ambiguous.
 * Appears everywhere in The Heptameron. Most stories Hand Wave it as "I won't name this guy because I used to know him once" or "I forgot her name, but anyway." Titles of characters abound, and proper names are few.
 * Several stories by Hans Christian Andersen.
 * Kokoro by Natsume Soseki.
 * Lucy Sweeney's Slummy Mummy column (and novel). The title character is called "Lucy" by others, but everyone else is named by description: Youngest Son and Husband on a Short Fuse, Alpha Mum and Alpha Mum's daughter, Smouldering Teacher, Celebrity Dad, and so on.
 * Beachwalker doesn't have a single named character. Instead, the characters are named after their roles, or after figures from the protagonist's favorite childhood story.
 * In Hilary Mantel's Wolf Hall the main character is never mentioned by his name, only ever being referred to as he or him. He is Thomas Cromwell, ill-fated advisor to Henry VIII (is there any other kind?), but the narrator never addresses him as such.

Music

 * Almost none of the characters in Ayreon albums are named; the exceptions are Merlin and a few characters with names based on the names of singers playing them.

Poetry

 * The Wedding-Guest and the Ancient Mariner in Samuel Taylor Coleridge's The Rime of the Ancient Mariner..

Theatre

 * Carl Orff's one-act opera Der Mond includes only one named character, who doesn't appear until the second half. In the Spiritual Successor, Die Kluge, none of the characters have names.
 * In the Spanish children's play El Principe Que Todo Lo Aprendio De Los Libros (The Prince Who Learned Everything From Books) all of the characters are called only by their role ("The King", "The Ogre" etc.) The only seeming exception is the protagonist, Principe Azul, which literally means "Prince Blue"- however, Principe Azul is the Spanish equivalent of saying "Prince Charming" so it doesn't really count as a name either.
 * About half of the characters in the fairy-tale-based Into the Woods are nameless (e.g. the two princes). Most of the rest are named because they are familiar fairy tale characters (Cinderella, Jack, Rapunzel, etc.); only Cinderella's stepsisters get somewhat gratuitous names (Florinda and Lucinda).
 * Edmond by David Mamet features just two named characters in its sizable cast: the titular lead, and a waitress named Glenna.
 * In Cirque Du Soleil's KA, the characters are called the Twin Brother, Twin Sister, Counselor, Nursemaid, etc. This makes sense as the show has no real-language dialogue anyway.
 * In the Richard Strauss opera Die Frau ohne Schatten, Barak is the only named character.

Video Games

 * Several modern videogames tactically (and sometimes not-so-tactically) avoid using the main character's name if you can choose it, otherwise voice acting would be impossible. For example, Final Fantasy X only ever uses "him" or "you" when referring to Tidus, and in Dragon Age Origins you're constantly being called "Warden" (or "Elf" or "Mage" or any other race and class specific things). In Mass Effect they do say "Shepard", but never your first name.
 * The hero of Final Fantasy called the Warrior of Light, and the hero of Final Fantasy III is "The Boy" and is titled "Onion Knight."
 * In both cases (though not in later versions for the latter), they were named by the player in their games of origin and have no canon names.
 * In Ace Attorney Investigations, Phoenix is never referred to by name, being only mentioned as "that lawyer" in Edgeworth's monologue. It isn't that noticeable, until Larry calls him "that guy in the blue suit", and Larry is Phoenix's best friend since childhood.
 * In an inversion, Shadow of the Colossus names everyone at least briefly except the main character and the Colossi. And even the main character is called either Wander or The Wanderer in the credits - it's not clear if that's actually his name or just a moniker.
 * Castle Crashers gives names to none of its characters, only referring them by what they are (The "X" Knight, The Cyclops, The King, etc.)

Web Comics

 * HERO is a partial example -- while there are a few named characters, some central and some not so much, there are also many major and minor characters known only by roles or titles.
 * Hanna Is Not a Boy's Name has {...}. He can't remember his own name. So he usually goes by Zombie by anyone too lazy to come up with anything creative or the random names Hanna gives him.
 * Hardly any of the characters in Gone With the Blastwave are named, and the two protagonists aren't among them. Furthermore, all the characters are Gas Mask Mooks wearing uniforms, so the emblems on their helmets are the only way they can be told apart.
 * ''Piled Higher and Deeper" includes many named characters but the central semi-autobiographical grad student has no name.

Web Original

 * Most of the anecdotes on Not Always Right, as the poster won't know the names of those involved, and it wouldn't add anything anyhow, so the names are usually a description - "Husband", "Wife", "Kid", "Mother", "Father", "Stoned Guy" - or just "Me", "Customer", "Cashier", "Manager".
 * The two friends from Two Best Friends Play. Since they are in the same room talking to each after already staring up a game, it makes sense that they would have already said their names to each other. This is dropped later on when their names are revealed as Matt and Pat.
 * Echo Bazaar is almost devoted to this trope. Characters with names other than "The Adjective Job Title" are limited to the Masters of the Bazaar (Mr. Thing, where Thing is what they trade in), the dueling opponents in the Black Ribbon, and a few others (F.F. Gebrant, Huffam, Esq., Madame Shoshanna, Mrs. Plenty) who have their own Twitter feeds and were thus grandfathered into the universe.
 * This is plausible true in-universe as well; the Traitor Empress has forbidden the use of her name, and it seems likely that, 30 years after the Fall, society has imitated this, with all remotely-fashionable individuals being referred to by role. All of those who have names are either on the margins of society or businesspeople (possibly aping the Masters rather than the Empress). Assuming you count semi-suicidal as being the margins of society.

Mythology

 * Many Jesus's parables are like this: the "sower" (of seed); the "man which sowed good seed in his field", also known as "the householder"; the "man" who sowed a grain of mustard seed; the "woman" who leavened her meal; the "man" who found a treasure in his field; the "merchant man" who sold everything for a pearl of great price; the "good Samaritan", and so on.
 * In fact, a number of people in the main narrative fall under this.
 * Referenced in Life of Brian, where Brian pretends to be a preacher, and says: "There was this man, and he had two servants..." A man from the audience asks what their names were.
 * Older Than Dirt: Surprisingly for a culture that put such emphasis and value on names, Ancient Egypt has a few tales with no named characters, such as the Tale of the Shipwrecked Sailor (Old Kingdom), the Wax Crocodile (Middle Kingdom), and the Tale of the Doomed Prince (New Kingdom).

Western Animation

 * Gargoyles don't have names,at least, they never used did in the time of Clan Wyvern. They acquire them later (to ease in communication, ). Goliath, and to an extent Hudson, don't seem all that fond of the idea.
 * I'd say Hudson is more open about this. When choosing names, he first denied it and sarcastically asked if the river needed a name. When told that they named the river "The Hudson", he just went with it.
 * By Word of God, humans invented personal names and gargoyles initially just regarded the custom as pointlessly absurd.

Live Action TV

 * In the Twilight Zone episode Five Characters in Search of an Exit, none of the characters have names. The Protagonist is known simply as The Major.