Rebecca is lovely. I think it has a touch of mystery about it, given the Daphne du Maurier story. But I much prefer it in full and I think it feels less dated that way. The only nickname I might possibly consider is Bex.
Ooh, the Daphne du Maurier story! Love that association. I would most likely use it in full form anyway, nicknames would be just for fun. Unless, my future daughter wants a nickname.