Curiously enough, Brian does have a deliberately non-posh nickname (used largely by his wife), though it isn't Brian, it's Fred. He, in turn, calls he Gladys. Meanwhile, his uncle the late and unlamented Edward VIII/Duke of Windsor was always known in his family as 'David', even though that was not his name.
He was called Edward Albert Christian George Andrew Patrick David, so it was actually one of his names.
Yes, but literally the last one and he was only given it for purely symbolic reasons (note that all of the last four - four! - names are of the Patron Saints of England, Scotland, Ireland and Wales).
Oh, so David is fitting for the Prince of Wales, isn't it? ;-)