Rebecca may not be as popular as it has been, but it isn't dated. It's pretty much timeless. More so than the Biblical
Hannah, which went through a long period of disuse before suddenly becoming very popular.
I think
Rebecca's a very pretty name. I don't like the nns
Becky or
Becca, they seem very babyish, and
Reba is laughably hillbilly. I've known plenty of Rebeccas, and quite a few went by just
Rebecca with no nn.