My sister-in-law's given name is Katie. She goes by Katie or Kate. My in-laws didn't want such a formal name. You could name her Kate or Katie, which are usually nicknames, and then nickname her Kitty.
Other K names (I don't think you have to use one with a "t" in it.):
Katyn
Kaelin
Kendra
Keira
Kendall
Kadence
Kaya
Katja
Karlie
Karolina
Kasia
Kalista
Kassidy
Kelita
Kiandra/Kiana
Kennedy