Members of the British royal family have no surnames. The Prince of Wales signs his name "Charles", although he could sign it "Charles P (for Princeps)". The Queen signs her name "Elizabeth R (for "Regina"). The family is of the House of Windsor; but eventually, those who are not entitled to the style of His/Her Royal Highness will bear the surname Mountbatten-Windsor (just as some of the descendants of George V bear the surname of Windsor).

As for Kensington Palace's address -- it, like all other royal palaces and residences, does not have a street address, probably because such an address is not thought to be necessary to get mail to where it belongs.