Nameberry.com has offered the following name suggestions. Boys: Albert, Alfred, Arthur, Frederick, George, Leopold, Philip; Girls: Alice, Caroline, Charlotte, Eleanor, Matilda, Maud, Victoria.
George might be a pretty likely choice since it's both a Greek and a British royal name and Frederick/Freddie is pretty popular right now in the UK. I can't see them picking Leopold. Matilda seems pretty unlikely but Maud is a recent royal name, though an ugly one, in my opinion.
I don't think they're likely to give the child a first name that is the name of any immediate relative, so no Elizabeth, Charles, Philip, Diana, etc. That seems to be decidedly out of fashion. I still think it will be Alice or Arthur, with the various grandparents' names as middle names. As far as godparents go, I would guess Prince Harry and Pippa Middleton and/or James Middleton as the sure bets and probably also members of their wedding party. Grandparents are traditionally never godparents, so none of the grandparents will be godparents.