I like
Alexis on a girl, not on a boy (it's too used on girls for a poor boy to carry throughout his life, but that might just be me).
I knew a girl once named
Alexis, but that's it.
I think you can get away with no nicknames. I have a name that could be shortened, but it never is, because I just don't call myself that...
I like
Alexis and
Alexandria! lol no help there.