I much prefer
Genevieve.
Jenna isn't awful but it's one of those names that strikes me as going to be very dated 15 and 20 years from now.
I do like
Jennifer how ever and with the nn
Jenny.
Jennifer is dated yes but I still think it's a great name and I honestly don't know that many Jennifers. I only about 3.
There's also
Ginevra "Gin" and
Virginia "Gin". Or
Geneva "Gen".