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.
"What have you been doing since you stole that antique TARDIS of yours, since you first landed on Skaro? Shouting 'Look at me!!! I'm not fighting a war!', while you battle the Daleks all the way through space and time."