The only time I've heard it used outside of as a surname (
Kay or
Kaye) is as a nickname. I knew a sweet older lady named
Kathleen and she went by "
Kay" and it was perfect for her. Also my friend
Sarah calls her sister
Katie (just
Katie, no full name) "
Kay" quite a bit of the time and it fits on her. I like
Kay on a girl, and it would actually age quite well, but prefer it as a nickname for
Katherine or
Kathleen. It would work as a nickname for
Kayley but that's so trendy right now.
Kay would be acceptable as a full name for a boy (as in the Authurian legends) but not really as a full name for a girl.