I've only ever known one
Aviva, and she didn't have a nn as far as I know. She was very beautiful, and trained as an opera singer, so the music association lives on.
I think
Xanthe,
Sylvie and
Aviva are a wonderfully pretty, feisty group! Go for it!
The only nn I can imagine would be
Eve. Or
Vivi, but preferably
Eve!