Other contenders that have floated around are the names Elizabeth and Diana (for Queen Elizabeth and Princess Diana, of course).
But now, a new and unexpected name has emerged: Grace.
Meghan has said that the couple decided not to find out whether they are having a boy or girl ahead of time, though the odds-on favourite is a baby girl.
But in an interesting nod, when we searched on the palace's site “/princess-grace,” it directed to a “Page not found” error.