I also love
Elizabeth. A lovely name, and versatile for nicknames too.
Elle is OK, but doesn't really seem to flow from
Elizabeth. (I know, I know,
Betty and a zillion others don't either.) Nevertheless, I still think
Elle is somewhat of a stretch.
Zizi -- well, I don't know. That one would require some thought.
Libby -- Cool. Cute.
Elizabeth Claire is one I considered for a girl. Then rejected because I though she would be E
Claire. You know, like the pastry, an eclair. I think I was overthinking that one! Anyway, yes,
Elizabeth Claire is my favorite.