Jazz as a full name is used slightly more often for boys than girls and has a distinctive, well, jazzy feel. Jazz is also occasionally used as a nickname for Jasper, much more often for Jasmine or Jazlyn. Could work as a middle name.

Musical choice that may be a short form of Jasmine or Jazlyn, or might stand on its own like this or as Jaz, the spelling used by tennis duo Steffi Graf and Andre Agassi.