Diseased Name

"It was Richard Le Gallienne, I believe, who once observed with regret that so many available euphonious and charming Christian names for men and women have been wasted on diseases. For example, where a more agreeable sound than that conveyed by the name Catarrh Carter or Diabetes White. Assuredly no current nomenclature is so soothing to the ear. Erysipelas is a prettier name than Alice or Mable or Grace, surely; just as Tonsilitis is a smarter name than George or Henry or even Montgomery. Which is the more mellifluous: Clara Jones or Pneumonia Jones, Gustave Smith or Appendicitis Smith? Which is the more musical: Susan Jackson or Diphtheria Jackson, Jacob Robinson or Syphilis Robinson?"

- George Jean Nathan

Many unpleasant diseases have Greek and Latin names that might make nice names for people if not for the associations. Such associations aren't so unwelcome in broad burlesques, which is where these names are most likely to be found.

Diseases named after people don't count.

Comedy

 * Anna Russell's "How to Write Your Own Gilbert and Sullivan Opera" had Pneumonia Vanderfeller as the name of the typical "British, piercing type soprano."
 * There used to be a whole genre of jokes/Urban Legends wherein a Funny Foreigner or black person would punch above their presumed intellectual weight and give their child a name like Eczema.

Comic Books

 * Angina and Bacteria, the wives of Geriatrix and Unhygenix respectively, in the Asterix comics.

Film
"Zoot: Oh, it's not a very good name is it?"
 * In Hudson Hawk, one of the CIA agents explains that their Code Names were diseases when they first started out. "Do you know what it's like being called Chlamydia for a year?"
 * At the end of The Addams Family Values, Cousin Itt introduces his new nanny: Dementia. Who turns out to be way too compatible with Uncle Fester... right down to being super-pale and having a bald head.
 * The Castle Anthrax in Monty Python and the Holy Grail.

Fanfic

 * My Immortal: Ebony Dark'ness Dementia Raven Way.

Literature

 * Lin Carter's Imaginary Worlds contains an essay in worldbuilding in which he suggests naming fantasy characters by taking names from mythology and disguising them a bit. By way of example, he takes the god Hermes Trismegistus and the prophet Zoroaster, blends their names together, and ends up with... Herpes Zoster.
 * Not a person, but in Igor, the entire civilization the characters inhabit is called Malaria.
 * In Hogfather, Ridcully mentions that he's got a distant cousin named Verruca, and there's also a small child named Verruca Lumpy. Whether they're the same character is unrevealed.
 * Narrowly averted in Carpe Jugulum, where we're told "There'd be a Chlamydia Weaver toddling around today if her mother hadn't suddenly decided that "Sally" was easier to spell".
 * The title character of Fever Crumb explains that, when she was born, it was fashionable for children to be named after ailments that their mothers suffered during pregnancy. Hence such names as the titular Fever, Diarrhoea, and "Craving-For-Pickled-Onions McNee".
 * Charlie and the Chocolate Factory: The resident Spoiled Brat is named Veruca Salt. It even gets pointed out by Wonka himself!

Live Action TV

 * Like the aforementioned Veruca Salt, the fourth season of Buffy the Vampire Slayer had several appearances by a werewolf named Veruca.

Tabletop Games

 * Anthraxus is the name of the leader of the Yuggoloths/Daemons in Dungeons & Dragons.

Theatre

 * Woody Allen's play God uses this for the Theme Naming of its main characters: Diabetes, principal actor of the Show Within a Show; Hepatitis, its writer; Trichinosis, inventor of the Deus Ex Machina; and Bursitis, the unfortunate actor chosen to play Zeus.

Video Games

 * This is the Theme Naming scheme for the Furons in Destroy All Humans!. Diseases and fungi are both used.
 * In Magical Girl Lyrical Nanoha A's Portable, Hayate's Evil Twin wields a magical staff named "Yersinia Kreuz".
 * Appropriately enough in Dragon Quest IX: Sentinels of the Starry Skies, the mayor of the town of Coffinwell has a name like this. It is Mayor Laria. To avoid explaining the joke, readers are instead invited to read the name aloud.

Western Animation

 * Thrax in Osmosis Jones. Justified, as he is a virus.
 * The Looney Tunes short "Knighty Knight Bugs" has one of King Arthur's knights named Sir Osis of the Liver.
 * There's an Arthur character named Rubella.
 * On Family Guy, the morbidly obese son of the Pewterschmidts' maid is named Diabeto.
 * In the same vein, Cletus the Yokel from The Simpsons has a morbidly obese cousin named Diabetty.

Other

 * "Alexia" is a variation on Alexandra, Alexis et al that's also the medical term for loss of the ability to read.
 * While "Amelia" is Latin for "lacking a limb", the given name is actually derived from German for "work", making it a linguistic false friend.