I must say, that's an unconventional but groovy idea for a character! As for a name, maybe there's a name out there which can be used as a play on words for sex toys, maybe even something alliterative that goes with "cat," or if that doesn't fit you could use another language's word for cat or dildo. Meanwhile, all my dumb ass can think up for a name is "Pussy Whip" so here's hoping you can come up with something better :P

True, when all else fails, go for the obvious but pluck from synonyms and other languages! :D
I'll do my best to do better, although 'The Pussy Whipper' is already pretty dang good, man!

Now there's a cartoon series (or series of cartoons) I'd like to see!
Can't think of any good suggestions for a name tho'. I name my chars things like "Doris Dog", "Anna Anteater" etc, not very creative. Catharsis Cat? Nah...

Katana Kitty?

...
But she has no katana. ._.