It depends, according to the official royal gift policy
Prince Louis was given so many gifts from well-wishers at Sandringham on Christmas Day that he needed help from his father, Prince William, to carry them all — but do Louis and his older siblings Prince George and Princess Charlotte get to keep the gifts given to them by the public?
George, 11, Charlotte, 9, and Louis, 6, were joined by their parents Prince William and Kate Middleton and the rest of the royal family for the annual […]
Are George, Charlotte and Louis Allowed to Keep Gifts They Receive from the Public? – People.com