I reckon either Alexander or Arthur.
However, I reckon that they won't go for David. Besides the inanity of naming him for David Beckham, I think the Queen might be still sore about what happened with another royal named David, the one who eventually became (albeit briefly) Edward VIII. And in case you're wondering, he WAS called David at home, despite David being at the end of a ridiculously lengthy name.
Four minutes? That's ages! What if I get bored? I need a television, a couple of books. Anyone for chess? Bring me knitting.
-The Eighth Doctor, defiant in the face of death, in Doctor Who: The Night of the Doctor