The royals tend to use more traditional names, but I would love it they went for something slightly more modern. Also, with their last name being Mountblatten-Windsor, the first and middle names should have less syllables.
For a girl, Emma, Victoria, Madeleine, Merabelle, Jossalyn/Joceline/Jossalene, Sophia/Sophie, Alexandra.
My guess is that the middle name will be in memory of someone, like Diana, or refer to a popular royal name, like Elizabeth or Anne.
For a boy, they will probably pick something like William, Edward, John/Jonathan, David or Charles though I would prefer Andrew James, Nathaniel, Spencer or Thomas.
We should do some sort of lottery to see if anyone guesses part or all of the full name, just for fun. What if they have twins?! lol