Our cat that passed last yr was named Puddy:

His nicknames:

Pu-Pud
Puddin' Pie (lol)
Puddin' Pop

Our cat that is still with us, Baxter:

Bubby
Bub-bub
Bub
Chubby Bubby (my DH calls him that sometimes)
Chubba (aren't we just awful? lol)
Baby Kitty