I think that if it is a boy, they will almost certainly go with
George,
Edward or
Albert. I would bet a lot of my money on
George though. It is a very prominent name of the Kings in their line of the family and it hasn't been used on anyone else in their immediate family in the past couple of generations.
As for a girl, I would bet on
Victoria. Long shot names may be
Mary,
Margaret or
Alice.
I expect
Diana and
Elizabeth to be middle names.
As this baby will be heir to the throne one day, I very much doubt they will stray too much further than the above names. For subsequent children, I think you will be more likely to see names like
Arthur,
Eleanor,
Matilda,
Caroline etc for subsequent children.