It is hard to name pets isn't it???It took a while to name my puppy, my brother even suggested that we call my female dog "bic&h" well she is one, but the name sounds

So name the kitty after someone you admire, or after what she looks like....
So since kitty likes to bite, possible names can be:
かむ kamu (v5m) to bite, to chew, to gnaw, (P)
かじる kajiru (v5r) to chew, to bite (at), to gnaw, to nibble, to munch, to crunch, to have a smattering of
Or better names

おかし okashi (n) confections, sweets, candy, (P)
あめ ame (n) (hard) candy, (P)