I've always been a big supporter of classic names, but I also enjoy many names that are a bit more unique. The solution? Classic names, with quirky nicknames! My own name is Caroline, but I go by Carly. I've never met another Carly whose full name is Caroline, but I still love that I have both a classy full name and a cute nickname. - Created by CarolineGabrielle
Lissie is a diminutive of Elise. I can also see it being used for Lisa, Elizabeth, and probably a lot of other "Elizabeth" variants. I first heard it in the movie Matilda.
Kitty is a somewhat-underappreciated form of Katherine or Catherine, and could probably work for other Kat- names as well, like Kathleen, Katrina, etc..
Kit is a unisex nickname. It could be short for Christopher, a la Kit Marlowe, or perhaps it could be another Katherine variant.