The short answer is that they don't always, or at least not in the way the question suggests.

Take the two that you've provided as examples. George VI's full name, before becoming king, was Albert Frederick Arthur George Windsor (née Saxe-Coburg and Gotha); Edward VIII's was Edward Albert Christian George Andrew Patrick David Windsor (née etc.). In his private life, George VI had been known as Albert or "Bertie"; Edward VIII had been known as David.

George VI was one of only three modern British monarchs to take regnal names other than those with which they had actually been christened, with the other two having been his great-grandmother, Victoria (christened Alexandrina Victoria), and his grandfather, Edward VII (christened Albert Edward). Victoria chose her regnal name as a point of personal pride, it seems, while Edward VII chose his in deference to the numerous Edwards who had previously reigned rather than choosing Albert in homage to his late father -- who after all had only been the Prince Consort and not a king in his own right. George VI seems to have gone in the same direction as this, Albertwise, choosing to style himself after his own later father, George V, rather than becoming Albert I.

To answer your original question, usually this is done as a matter of homage and deference to the generations who have come and gone before. You can see from poor Edward VIII's full name that a very large number of people were being commemorated in his baptismal record, and this often led to the weight of many generations being foisted upon the coming monarch -- though of course he or she would have no reason to expect anything else. It all stands in stark contrast to something like the papal regnal names, which are chosen with an eye towards thematic significance rather than (a contextually impossible) heredity.

More mundanely, royal children often find themselves saddled with certain names for just the same reason that any child would. Many have been the couples who have lovingly decided to name their son or daughter after one of their own parents, after all, and the Georges/Alberts/Edwards of the royal world would be no exception.