The name Cate is a girl's name of English, Greek origin meaning "pure". Cate and is often added to lists like Video Game Names for Girls and discussed in our forums with posts like "Adding then Eliminating - Boys Themed".
From the experts:
Time was, even C-starting Catherines who called themselves Kate spelled it with a K, but Cate Blanchett changed all. Cate is now as acceptable as (but not as well used as) Kate. Cait might be short for Caitlin.