Im biased, cuz
Elizabeth is my name, and a family one too :). You don't hear it on little girls often anymore, but it's a great name to have, despite how formal and common it is already. She can go by many nicknames for sure(like
Beth).
Rebecca is sweet, I like it more than
Elizabeth, but I love it more as a middle name. Im not sure if I would see myself using it as a first, because its dated imo, I picture it as a mom name.