Buster (male golden) - Nux - short for Knucklehead, or Beast
Rodman, male, black lab mix (had him awhile back, and the kids who owned him for the first 3 months called him “Jordan,” so we thought we’d stick with a Chicago Bull name): Sodman (weird, I know), Rod-tard.
Moose, male, mixed between a Blue-Heeler and ^Rodman: Moosgers.
Cali, female, cat: Calwhore (ha, my fiancee hates that one).
Pepe, female, chihuahua and lord knows what else: PeePee Underbite of Devonshire (that’s her “show dog” name, she has a goofy looking underbite).
Jolt, male, cate: Joltersohn.
I don’t know how I come up with these damn names sometimes. 
Mostly I just call them “dog” or “stinky.”
Every now and then I will actually use their name.
Oreo, dog, male: Tiny Terrier Toes, Baby Bubble Bear, Dick Lickery, Big Puppy
Cats:
Nimitz (male - Russian Blue X): Top cat, psycho
Dewey (male - ginger/white DSH): stealth cat, fuzzbutt
Mishca (female - DSH): noisemaker, whiney
Anushka(top) (Female - Himalayan Exotic): furbag, no-nose.
You got duds. Every cat I’ve ever owned has responded to his/her name, even the one we caught as a feral kitten.
Also keep in mind that “responding” might be opening an eye to look at you, as opposed to coming when called. They are cats, after all. You’re not the pack leader, you’re staff. 
Odie the dog is “Buzby”
Kali the dog with bad breath is “Kalitosis” (he’s so gross-is)
Pippin the dog is “Scribby-doo-Biscuits” or Scribby-doo" for short.
Minnie the dog is “Moo”
Fluffy the cat is “Fluffinator”
As someone once said, “Dogs have owners; cats have staff.”
Zuk, a 60lb-ish 1 1/2 yr old pit bull terrier. His nicknames: Zuk the Duke (of Harding), Zukie, (Zukie) Dukie Doggie, Zukowski, Stanley Zukowski, Dr. Stanislaw Zukowski, Velvet, Jingles
Oh wow. I thought there was something odd about that doctor I saw last year. I should have reported him when he asked me to rub his belly, but at the time, it seemed harmless. He didn’t talk much, just panted.
Since I aquired my cat very gradually. She was a stray that slept in the garage and I started feeding (you can guess how this ended) I never got round to giving her a name. An early option was “Scruffy” - because she was. But after being fed properly for a while and de-flea-d she wasn’t anymore. These days she’s quite plump and sleek. So she gets called “Kitty” qualified by what ever she’s up to.
Scratchy Kitty
Shouty Kitty
Hungry Kitty
Poopy Kitty
Buddy the dog: Old man, Papaw, Bud
Loki the dog: Little Guy, Chachi, Cheech, Lokidoki
Charlie the (roommate’s) dog: Chahhhrles, Sir Charles, Charlie Pace
Miso: Meesh, Babygirl, Snugglebunny
Mouse: Mouseling, Gray Girl
Raven: Blackie, Blackitty
Meeps (yes her name is MEEPS): Meepmeep, Beepbeep, Squeaky, Lil Girl
Moose: orange & white male dsh. Mr Cat, Fuzzbut Orange L’Miao (pronounced with cheezy fake french accent), bad cat
Mimi: cream calico female dsh. Madame Chat, pretty girl, bad cat
So handsome! And he’s a doctor!
Maguire: 12yo Yellow Lab: ‘Guwhy,’ 'guire, puppy-dog, old man, dingleberry (usually when he is giving me that earnest, but dumb Lab look).
Maggie: 5yo Chiweenie. Maggie Mae (her full name), booger-butt, boo-boo (well, what my wife calls her), baby-dog (my preferred). Ironic, my wife choose her because she wanted her own dog, but Maggie Mae, is now MY baby-dog. Sleeps on me, snuggles with me, prefers me, pretty much across the board. I come home, no matter how late, and Maggie will leave my wife’s lap and demand to sit in mine.
Dog, F, named Ellie - Ellie Mae, Ellzey Mae, Baby Girl, Angel Pie, Little Bit, Squeaky(she makes the sweetest little squeaky sounds when she yawns), Honey Bunny
Delilah the Pekingese (Dede, Dede weedy, Dede wider, Ziti)
Ian the Corgi/Black lab mix (Een, Bean, Grean bean, Ian Bein)
I love my doggies. 
Boo, rabbit, female: I call her ball of fluff, woggler, meerkat, and sweetieface. My dad calls her Boo boots, Boo Boo Bear, bear, horse, and camel.
I sometimes complain that she must be very confused about what species she is, what with all the animal nicknames. But then again, we’d had her for three weeks before the vet told us she wasn’t male and we subsequently changed her name (from ‘Abu’), so she’s probably confused about most facets of her identity.
Our dog is a chihuahua named Ren, after the character from Ren & Stimpy. We have variously called him:
Prancer - because he totally does this little prance whenever he walks around. Other people have commented on it too.
Sir Whine-a-Lot - because he whines whenever I leave the room and he can’t get to me, such as when I need to use the bathroom
Your Highness or Your Majesty - said dripping with sarcasm when he is being demanding
Little Mister - what my husband sometimes calls him when he gets home from work and Ren goes to greet him
Our cat, Sophie, is a mix of Russian Blue and British Shorthair. We have called her:
Miss Chubby Cheeks - I call her this because she has the typical stocky build of a British shorthair. Although my husband tries to “correct” me and say she has “fluffy” cheeks, not chubby. 
The Cat from Ipanema - Another nickname from me, because she really “swings” and “sways” when she walks, like the song. Although my husband describes it as a sashay, so maybe I should call her Rupaul.
Madame - from the old saying that dogs have owners and cats have staff. Us lowly staff members sometime call her Madame while getting her food, etc.