I agree with others that [name_f]Eve[/name_f] fits your criteria and feels the best option for you. From your runners up list I think [name_f]Nora[/name_f], [name_f]Juno[/name_f], [name_f]Jane[/name_f] or [name_u]Zoe[/name_u] would work well. [name_f]Eliza[/name_f] is my personal favourite. Good luck!
If it helps at all, my name is [name_f]Eve[/name_f] and the [name_m]Adam[/name_m] and [name_f]Eve[/name_f] jokes are actually few and far between. It’s never been a burden to have my name and there have never been any issues. I actually love it because everyone knows how to spell and say it but it’s not super common!
Also, my parents are not religious and nobody has ever considered my name to be overly biblical to the point where that wouldn’t make sense.