Personally, as a fellow
Genevieve lover myself, my favorite nickname idea for it is
Ginny like
Ginny Weasley. Jenna/Genna is so ordinary, generic and 90s dated. Why take away from the majestic feel with boring
Jenna? I'd say
Ginny,
Evie, or even possibly
Vivi but
Jenna is just unappealing to me.