Probably after either someone they know and are close with, or past English monarchs. For girls, I'll say Diana, Elizabeth, Beth, or Catherine. For boys, I'll say William, Harry, Henry, Charles, or John. Personally, if it's a girl, I think it'd be cute to name her Diana after William's mother.
My guess is a name that they like. But seriously. In the U.S our Constitution prohibits monarchy and for good reason. I understand that the British keep their monarchs just for show but I think it is time that we stopped idolizing monarchy. Let us not promote the idea that we should exalt people who are born into a privileged class.