Have you considered the initials? A first name starting with J will give you JP, which at least in Australia stands for Justice of the Peace. Which I think is kind of funny sounding.
Personally, I'd pick a non-"J" name. I'd also avoid KP (kitchen patrol), BP (blood pressure/petrol company), GP (general practitioner), HP (pencils), LP (long play/records), MP (politician), PP (pee-pee), TP (teepee), and UP (up).
But then, initial combinations might not bug you the way they bug me! Go with whatever sounds right to you. Though please do avoid a P first name - being nicknamed "pee pee" wouldn't be fun when a child.
Apart from that, I'd avoid all the Harry Potter book names. So, no "Harriet" or "Ginny" or "Lily" Potters.
If you're sticking with J names, I'd pick something classic, or a little fancy, and long in length. Jessica is nice!
:)Bronwyn