White Ivy.
(Serious prediction: Spencer)
Irving.
I don’t know, that sounds awfully Catholic…
I really, really like James.
Robert. Has there ever been a King Robert in England? Why not?
D’Brickashaw.
I just like saying it.
I have to admit, Joffrey would be hilarious.
Knut
Alfred
Albert
George
Considering he’s likely to have four given names and that’s also one of his grandfather’s I would not be surprised it was one. We are actually speculating on what will be his “main” name.
Barack Hussein Mountbatten-Windsor
I think James is out because Prince Edward already has a young son named James.
Moved Cafe Society --> MPSIMS.
Dweezil or Ahmet Rodin
Had it been a girl, Moon Unit or Diva Thin Muffin Pigeen.
HRH Philip James Henry George, Prince of Cambridge.
“Booger,” to his friends.
Rudiger.
Where I merged it into the existing thread.
Wouldn’t James be out for being too Jacobite? Have there been any Jameses in the royal family since the Glorious Revolution?
They should go really old school.
Arthur.
Not Aethelred?
I’ll vote for “Botfly” or “Giardia” - something appropriate for a small parasite.
Arthur George Henry Michael. Called Georgie or Mikey. Becomes King Arthur one day (without the sword in the stone bit). 
No, but there was at least one in Scotland – Robert the Bruce, founder of the Stewart dynasty. (That didn’t die out until Queen Anne!)