Timeless.
BookMeOnTheSudExpress summed it up for me.
I think people are confusing "had a run of popularity 30 years ago" and "dated". Dated would be something that was never a classic to begin with.
4000 years old, as bridgetreilly said. Yes, it's biblical. She was the wife of Abraham's son Isaac, and the mother of Jacob and Esau.
I love Daphne Du Maurier's book Rebecca and the Hitchcock film version. Becky Sharp in Vanity Fair is one of the greatest characters in English literature.
Good classic name. Go for it!