Why Genna, may I ask? When I see names like it, my first instinct is always to use a hard G (as in Gilligan), unless it's short for something like
Genevieve.
Jenna would be a far easier name to live with, I think (and I find it more aesthetically appealing, personally, but that's just me).
I'm not sure what sorts of names you're looking for, so some random ideas:
Genna
DesireeGenna
MarianGenna
LaurenGenna
BridgetGenna
CalypsoGenna
WinifredGenna
NoreenGenna
WrenGenna
FleurGenna
IvyGenna
CleoGenna
RubyGenna
HilaryGenna
ReginaGenna
CallistoGenna
Colleen
Array (doesn't help that she sees Genna and thinks "Barefoot Gen," one of the most harrowing after-the-atom-bomb films she's ever seen)