Well, I've actually met (mostly online) people who have converted and chosen a Christian name.
They keep their old given name in there somewhere (as a middle name usually), but I don't think there's any hard and fast rule about it.
A new Catholic should be happy to identify with a patron saint in heaven, and should look forward to starting a new life. A new life deserves a new name. (Saul --> Paul, Simon --> Peter, etc.)
Ask Spouse of Jesus what she would do, if her dream came true and she was baptized.
Think about it, though -- what do most pagans use for names? They're not naming after saints in heaven (or even "saints" in their own version of heaven) They usually have simple, degraded names, with meanings like "rice field", "worker", "on the farm", "short", etc.
Why not give that up in favor of a Saint's name?