Cats

A.L.F. (Alien Life Form)
Airhead
Alcatraz
Ali Kat
Alfalfa
Amigo
Anchovy
Axl
Cat Ballou
Charmin
Crank
Bam-Bam
Bambi
Bambino
Band-Aid
Barfly
Barnacle Bill
Bashful
Beaker
Bear Cat
Beattlejuice
Big Foot
Big Mac
Blimp
Blotto
Bogart
Boo Boo
Boomerang
Bouncer
Budweiser
Bullseye
Bungie
Butterfingers
Cat Stevens
Catfish
Catnip
Charley Brown
Chewy
Chi Chi
Chicken
Chiclet
Clod
Clawless
Clueless
Comet
Confucius
Dante
Dizzy
Einstein
Evinrude (purrs a lot)
Figaro
Fishbone
Fletch
Ginsu
Godzilla
Inferno
J-Lo
Kami Kazi
Klingon
Linus
Monkeybrains
Muffintin
Muppet
Paws Scaggs
Pez
Pixel
Purrsha
Skittles
Slick
Slinky
Smudge
Snagglepuss
Splat
Velcro
Wasabi
Weezer
Wizzer

Dogs

Ammo
Archie
Askim (What's his name?)
Blotto
Blubber
Bogie
Buckshot
Buzzsaw
Chewme
Chunky
C.H.U.D. (cannibalistic humanoid underground dweller)
Cujo
Deogee (De=D; o=O; gee=G)
Ding Dong
Dolittle
Eddie
Elvis
Farter
Furball
G-unit
Gator
Gizmo
Gomer
Gonner - a rescued dog
Hobo
Holmes
Homey
Hooch
Hulk (Big Dog)
Jughead
Kegger
Keno
Klutz
Knockout
Knuckles
Nightmare
Ninja
Nugget
Nutt
Ogre (not so pretty ones)
Ozzy
Patches
Paws Scaggs
Peanut
Pecker
Popeye
Puddles
Rambone
Rimshot
Sarge
Sausage
Schnapps
Showoff
Shredder
Snoopy
Sputnik
Squeeky
Stay (try it)
Target (dark patch on eye)
Taz
Toots
Wookie
Zed
Zeppelin
Zeus
Zippo
Zorro

Pairs - Cats

Bartles and James
Ben and Jerry
Bonnie and Clyde
Buster and Babs
Cagney and Lacey
Calvin and Hobbes
Cheech and Chong (Siamese)
Hugs and Kisses
Itchy and Scratchy (fish too)
Salt and Pepper
Sears and Robuck
Smash and Crash
Mona and Lisa

Pairs - Dogs

Heckle and Jeckyl
Lucy & Ethel &/or Ricky
Rhett and Scarlett
Rif and Raf
Rocky and Adrian
Thelma and Louise
Thunder and Lightning
Tigger and Eeyore
Ying and Yang (1 black 1 white)