His parents picked a name fitting for a Prince Consort. His grandfather, fully expected to be "King Albert Edward", chose to be Edward either out of some very complicated psychology with both of his parents and/or as he politely said, that his father's name should stand alone.
In George VI's case, he had the option of being the first King Albert or going with continuity, as said. He chose not to rock the boat (more). But in neither case was it because of 'not regal enough'.
And they are the only two British monarchs who've had "regnal names", aside from Victoria who simply didn't like and wasn't known as "Alexandrina". Charles not reigning as Charles would still be the exception, not the rule.