I don't think the association is too much- it's definitely there, but the name is used enough in other places for it to be overpowering.
Juliet Eve is very pretty... some others:
Juliet MayJuliet BelleJuliet PearlJuliet HopeJuliet MaeveJuliet LivJuliet RuthJuliet KateJuliet Cate
Juliet May is probably my favourite, but I think
May might (unfortunately) have the potential to become another
Rose or
Grace as far as mns go...
Also, this is a little off-topic, but my brother was going to be
Juliet Rose if he was a girl (he's
Jesse Tyler now, and was born ten years ago).
Shannon