Of course!!!

Dogs

Shadow: Shabadow dog, Shadow Baby, Cow dog
Kyra: Ky, Kyra kid
Jack: Jack dog, Black dog, Doofus, Goof-head, J dog, JJ (His real name is Jumpin' Jack Splash) Jackie-loo (in a really high pitched screach!) JackJack
Micki: Boogaman, Booga, Mick, Mickers, Meeester, Meester Mouseman!!
Mini: Min, Minard, Princess, Face, Mouse, MouseMouse

Cats

Jasper: Jaspy, King Tut, Jaspurrrrr, Jasperkitty
Lassie: Fat cat

foster kittens...
Batman: Batcat
Motchka: Motchygirl

The guinea pigs really don't really have nicknames, Henry I call Henners, Elvis - Elly, Mo - Mokey man