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I think of it as a rather endearing nickname, and I wouldn't mind it as a first name either. I think it's usable as a nn for any name really. I had a best friend in middle school who went by Kitty (her real name was Stephanie) and I think it was a self-given nn, possibly chosen because her surname is related to cats.
It works on grown women as well in my opinion, mostly because of the association with Kitty Forman from That 70's Show.