I always thought that there were kind of extenuating circumstance surrounding the names they had/the names they went with in regards to the two Berties, Edward VII and George VI.
Edward, previously known as Prince Albert Edward, had a typical Hanoverian relationship with his parents - I wouldn't exactly say that he liked them or that they liked him. He was named in part for his father, and it was his mother's desire that he be crowned "King Albert Edward" and that all subsequent Kings be "Albert something" (hence his first son's name being "Albert Victor"). Except, can you really blame a guy for not wanting to be known (for the rest of your life and really the rest of history) by the name of a guy who 1. you didn't really like and 2. you were accused of causing the death of, in accordance to the wishes of 1. another person you didn't really like who 2. did the accusing?
As for George, he came to the throne during a crisis. His name choice didn't necessarily reflect his feelings regarding his name but rather a desire to stress the connection with his father.
Charles has, to the best of my knowledge, no issues regarding his name and no need to stress any continuity with any of the Georges. His mother named him Charles, suggesting that she wanted him to become Charles III, but there isn't a Hanoverian relationship there. Furthermore it's the name that he's been known by for 64 years. Yes, both Edward and George were known by other names prior to ascending, but I always felt more like they were known by their titles - The Prince of Wales and The Duke of York - more so than any name. Charles, however, is known by his name.