Tribute to Fido

[Bubbles] was a mongrel, but a really nice dog, and she had fitted so well into our lives. So I brought her into Xanth, where she can live the life she could not continue with us.

—Piers Anthony, author's note of Demons Don't Dream

Most people love animals, especially their pets. Some authors may even put some sort of reference to a real-life animal in their work. Most often, it will be their own pet, either as a memorial or just because they love him that much.

It may be just the animal's name, similar to the human equivalent, Tuckerization. This is justified in a film if the pet themselves is playing the pet named after them; after all, it's much easier to get an animal to respond to its own name. The whole animal, not just the name, may be put into the work as well. Or, perhaps, they based an animal character off a real-life one, such as its appearance or mannerisms, even if they didn't use the name.

A note for the geeks among us: This trope has nothing to do with the FidoNet.

Examples of Tribute to Fido include:

Comic Books

The DC Comics miniseries A Superman for All Seasons, by Jeph Loeb and Tim Sale, gave teenaged Clark Kent a dog named Shelby, after Sale's own dog. It was a two panel gag, but Shelby later became more notable as the golden retriever in Smallville.

Film

The character Indiana Jones is named after creator George Lucas's dog Indiana, who was also the inspiration for Chewbacca. There is also an in-universe example that reflects the Real Life situation: in Indiana Jones and the Last Crusade, it is shown that the character chose the nickname "Indiana" after his family's dog.
- This was taken even further in Temple of Doom: Willie was the name of Steven Spielberg's dog, and Short Round another crew member's.
In Disney's Dumbo, it is implied that Dumbo's father is Jumbo, a famous elephant that appeared first at the London Zoo then at the Barnum and Bailey Circus. Dumbo was supposed to be named Jumbo Junior, but ended up being known by a mocking nickname instead.
Of the Justified due to the animal playing the character variety, the dog Jed played the eponymous creature in The Thing. He's also been in a couple other films. Interestingly, the dog is never named onscreen (only in the credits), but fans of the movie have taken to referring to the dog with this name.

Literature

While Piers Anthony was writing his Xanth novel Demons Don't Dream, his dog Bubbles died, so he decided to put her into the book at that point. Part of his explanation can be seen in the page quote. Mare Imbri is also based on Blue, a horse he owned at the time. Blue died right before he started writing the same book, so, as he pointed out in the author's note, it seemed right that Mare Imbri would lead Bubbles into Xanth.
There was a contest for the Joe Grey mysteries for fans to send in descriptions of their pet cats. Three were randomly selected as occasionally-recurring characters.
In the Warrior Cats series, Brambleclaw and Sorreltail are named after author Cherith Baldry's cats, Bramble and Sorrel. Sol's appearance is based on a cat named Aslan, and Millie's appearance is based on the pet of one of Vicky Holmes' coworkers (her name comes not from his cat, but from the fact that he is a fan of the Millwall soccer team).
Dodie Smith's inspiration for The Hundred and One Dalmatians was her dalmatian Pongo; naturally, she put him into the book as the main character.
Lady Jane, the evil-tempered gyrfalcon who is constantly attacking Hodgesaargh in Discworld, is named after a real falcon, just as Hodgesaaargh is named after a real falconer.
Jean Craighead George has based many animals in her books on pets she's had in the past. One notable example is that the behavior of the owl in There's an Owl in the Shower is based on a pet owl, Yammer, that she used to have. She tells stories about her wild pets in The Tarantula in My Purse".
In Sideways Stories From Wayside School, there is an in-universe example: a boy named Nancy, who dislikes his name, trades names with a girl named Mac, who disliked hers because she had been named after a dog.
In Homer Hickam's Rocket Boys autobiography trilogy, there's a scene where the author's mother is painting a mural on the wall, adding in some pets of theirs that had died, such as a fox named Parkyacarcass.

Live-Action TV

Ubu Productions is named after producer Gary David Goldberg's dog Ubu Roi, a black labrador retriever. The Closing Tag for Ubu's productions is a photograph of Ubu Roi with a flying disc in his mouth. Along with the picture is Goldberg's voice saying "Sit, Ubu, sit! ...Good dog!", followed by the sound of a bark. This can be seen here.

Music

Havalina Rail Co. had a song about Laika, the Russian dog who became the first animal in space. (Though Havalina spelled it "Leica".)

Newspaper Comics

Charles Schulz based Snoopy on his childhood dog, Spike. Later, we meet Snoopy's brother, who is named Spike.
The cat, Horse, in Footrot Flats was based on a real cat who hung around the author's farm.
In Calvin and Hobbes, Hobbes was inspired by one of Bill Watterson's cats. He explains in the 10th Anniversary Book:

Hobbes was very much inspired by one of our cats, a gray tabby named Sprite. Sprite not only provided the long body and facial characteristics for Hobbes, she was also the model for his personality. She was good-natured, intelligent, friendly, and enthusiastic in a sneaking-up-and-pouncing sort of way.

Video Games

The police dog in the first Ace Attorney game is named after the creator's Pomeranian Missile. He doesn't do anything useful, but he does eat all of Larry's hot dogs.
- A-dog-named-Missile returns (though not the same Missile) in Ghost Trick as a full-on main character, this time with additional Pomeranianness.

Web Comics

Kirby, Cole's basset hound in PvP, is named after (and modeled on) Scott Kurtz's own basset hound Kirby.
Guineas, one of Grace's siblings in El Goonish Shive, is based on a friend's guinea pig, due to a lack of ideas.
Both of the cats in Two Lumps are based on the author's (now deceased) pets.

Web Original

On Honorable Hogwarts, the character of Lucy Frost is named after her creator's cat. As in, the cat's full name... the guy behind the character is actually named Frost in Real Life, so Frost is also the cat's surname.
The creator of the Hampster Dance website made it (and named it) in honor of her hamster, Hampton.

Real Life

The word "jumbo" as a synonym for "really big" is a reference to the elephant Jumbo that was mentioned above.
John Wayne's nickname "Duke" comes from a dog he used to own, even back before he became famous.