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.
I've lived for over 2000 years, and not all of them were good ones. I've made many mistakes. And it's about time I did something about that.
-The Twelfth Doctor, Doctor Who: Deep Breath