I am hoping for a boy simply because George is the only boy in his generation. Savannah, Isla, Mia and Charlotte - he needs a boy within a close enough age range to be friends and to play with. James is ok but he is still his father's cousin and not his generation.
I don't think they will use a name of an existing prince - so no Philip, Charles, William, George, Harry, Andrew, Edward, Richard or Michael as a first name.
That means spreading the new a little wider to find a family name - Christian (both the Queen and Philip are descended from Christian IX of Denmark - but already in use in Denmark for a future King) but it isn't a name used in the UK; John - bad history so not that popular; David - a nod to Wales and not used as a first name in the UK - although it was Edward VIII's family name; Albert - the Queen's father is fairly obvious there;
So I would go with - David Albert Charles
For a girl using the same criteria I am ruling out - Elizabeth, Charlotte, Beatrice, Eugenie, Anne and Alexandra.
Victoria - maybe but then there could be confusion with the Crown Princess of Sweden - even though it is also Philip's grandmother's name; Mary - a nod to the Queen's beloved grandmother; Alice - Philip's mother and great-grandmother; Caroline - a nod to Catherine's mother
I would go with Phillipa though - after Catherine's sister AND William's grandfather
so
Phillipa Alice Victoria