What ever it is, it'll most likely be long with 2 or 3 middle names.
Immediate male family full names (not including titles) are:
William Arthur Philip Louis Mountbatten-Windsor (Dad)
Henry Charles Albert David Mountbatten-Windsor (Uncle)
James William Middleton (Uncle)
Charles Philip Arthur George Mountbatten-Windsor (paternal Granddad)
Michael Francis Middleton (maternal Granddad)
(Mom's full married name (without titles) is Catherine Elizabeth Mountbatten-Windsor.)
They could go with any combination of names or mix in something new.
I'm fairly certain they won't go with Prince Moon Unit or anything trendy.
Additional:
I highly doubt Spencer will be in the running - grandmother's maiden name got dropped when she married.
Diana's full married name (w/o titles): Diana Frances Mountbatten-Windsor
Additional:
The choice has been made:
George Alexander Louis Mountbatten-Windsor