Gavin is fine for a boy but doesn't work on a girl. I think it would have to be short for something.
Gavina: isn't on BtN but
Gavino is and this would just be a female version (comes form
Gabinus). But I don't think you'd actually want to use this name because people would always switch the G and V as a joke and it would stop being funny by the 5th time she heard it.
Gavriela /
Gavrila: you could get
Gavin by adding "in" to the first syllable, in the same way
Robin can be short for
Robert. It's pretty contrived though, and she'd probably just be called Gavi.
I like
Raven on a girl or a boy.