Well, there is Alex and then Lexi those are pretty much the two (and probably only) main nicknames for the name Alexis, and I should know its my name lol
Yes, for a girl.
Addison or Amber
Alecia.
D. then initial for last name.
Emmie
Faye or Fifi could be cute nicknames for the name Faith.
Nicknames are usually shorter than the real name, but with Zoe there isn't much to trim off.
Alexis Coria goes by Lexy.
Alexis Kupka goes by Lexie.
Alexis Lane goes by Lexi.
Alexis Albert goes by Lexie.
Alexis Dahlin goes by Ekki.