I have long wondered: their given names were David and Albert - Why did they change their names? why could they not be King David and King Albert? Or perhaps the question should be reversed: why were they not given names like Edward or George or Charles or William etc etc? Or perhaps there is no answer...
I don't know about George, but King Edward VII was born Albert Edward. I read in the paper this weekend that they went with Edward simply because Albert sounded "too German" - but that sounds a bit simplistic to me!!
Fashions for names change. Edward VII was near retirement age when he finally acceded. And yes they could use their own names if they chose, but they chose not to. David was far too biblical. Edward vii didnt use albert because he didnt like his father much. And Charles has never been a lucky name for a king. Tradition has it that John isnt used again, ever.
The reason they change it is the same as the pope: they feel there are percieved characteristics that go with the name.
Queen Victoria (bless her the nutty old thing) wanted all her male issue to be called Albert (this included grandchildren in the line of direct sucession). Monarchs have always been alowed to choose a name by which they will reign as incitatus says this is often to do with comparision with other monarchs.
BTW there have been several names that were only used once Stephen, Matilda (if you count her as queen), John, Anne and Victoria.