Kit may be a male or female given name or a pet name for a number of other names.  These are the main ones:

1. English variant of Kat, a pet name for Katherine/Katharine/Catharine/Catherine [q.v.].

2. Scottish male and female pet name for Christian [q.v.].

3. Irish pet name for Kathleen [q.v.], via Kat.

Kitty is a pet form of Kit and for several of the above names.