Harvey - James Stewart’s rabbit
Ribsy - Henry’s dog from the kids’ book series of Henry and Ribsy
Battlecat - He-Man’s cat, alter ego of Cringer
Brain - Penny’s dog from Inspector Gadget
Daisy - Dagwood Bumstead’s dog
I once had a beloved cat named Pete, short for “Petronius Arbiter,” from one of my favorite SF books, The Door Into Summer by Robert A. Heinlein.
Crap…beaten to Battlecat.
Buck is also the name of the Bundy’s dog on Married With Children.
Gort’s a robot, not an animal, and from The Day the Earth Stood Still.
Is this Harvey the invisible/imaginary rabbit from the movie of the same name?
Orson was the name of the pig from the farm segment of the old Garfield and Friends cartoons.
My mother has a horrible devil-cat that I’ve nicknamed “Church,” after the scary undead kitty from Pet Sematary.
No.
Woosh.
I did say that these were dogs and cats — or at least doglike and catlike.
Harvey, on this list, is not a rabbit, nor is Orson a pig, nor Gort a robot.
Good ideas, though. 
I don’t know if this is the dog you’re thinking of, but Fluffy was Hobo’s first name in in the book Summerdog Comes Home.
Llyan is the giant cat from the Prydain novels.
Wordsworth W. Wordsworth is one of the cats from the Heathcliff cartoon, the one that rhymed all the time.
And is Otto’s Cat the cat from Cat and I?
Let’s see, on these remaining ones, I should give some hints.
Ginger and Pickles
Harvey (hint: Drew Barrymore)
Baby Cinnamon
Gort (hint: Matt Dillon)
William the Conqueror (hint: Karl Malden)
Asparagus
Lipshen
Orson (hint: Chris Snow)
Mr. Underfoot
Frank (hint: Will Smith)
Frank is the pug from the Men In Black movies.
Are Ginger and Pickles the cat and dog from the comic Pickles?
Anyone remember Freeway?
Yep, the little dog from Hart to Hart.
How about Clarence? Although he may not qualify as a pet.
“Lipschen” should probably be “Liebchen,” Anjelica Huston’s cat in “The Witches.”
Isn’t Mr. Underfoot one of the Smith family cats in “To Sail Beyond Sunset?”
I’m withdrawing Cat from consideration. I thought it was fairly obvious (Holly Golightly’s unnamed cat from "Breakfast at Tiffany’s) but I guss not.
That’s Muffin and Roscoe.
As for Mr. Underfoot: correct author, but isn’t he in the book Friday?
Asparagus, from Cats?
The only Fluffy I thought of was the three-headed dog from Harry Potter.
It’s probably just a popular name for fictional cats.
Oh, and Pyewacket is Kim Novak’s gorgeous Siamese cat from Bell, Book and Candle.
Hmmm… WAG, is Harvey the framing device cat from Cat’s Eye?
Ginger and Pickles are chickens - Chicken Run
Pyewackett was also an actual cat in a 17th century witch-trial. Matthew Hopkins, the Witch Finder General, said that it was a name ‘no mortal could invent’.