Eve and its derivatives may be quite trendy at the moment, but it is also a longstanding classic name. My granny was Evelyn and she was born in 1920! Woudl have been on my list if DS had been a girl, except would have been daft with DH's name.
It's a lovely name - and I wouldn't worry about being of the moment - I was called Sarah in the 70s and have always been surrounded by hundreds of other Sarahs but didn't really bother me. Only thing I would say is would you want two daughters with the same initial? I had a friend at uni and her and her two sisters were all something beginning with S and it really annoyed her - cos for example if something came addressed to Miss S. xxxx then they wouldn't know who it was for. A small point.... but worth thinking about.