Here are some pet names I plan to use at some point.
Note: Cats names are more fun in a sense, because cats don't answer to their own name anyway, so you don't have to worry about it being too long or complex for them to understand.
Castor and Pollux (twins!)
Cat with No Name , or CNN for short, so that when I introduce her I can say, "This is CNN."
Sparta (see my reasoning with CNN ... also, I would want to own Sparta and CNN at the same time, for obvious reasons)