I'm one and it's done me ok for 47 years. I have a strong dislike for most of the shortenings, but that isn't a problem- I introduce myself as Rebecca and 'correct' (nicely, and politely) people who take it upon themselves to call me Becky. I'd say timeless - wouldn't think it at all odd to hear a baby being named it, and I know people of widely varying ages with it.
But what is it with people calling you Rachel???!! Happens all the time! Just this week I had a(nother) email from someone replying to my rebecca@.... email address with 'Hi Rachel'. They don't sound remotely alike!