I believe it was common for monarchs to take on a Reginal name that wasn’t necessarily the name they used say-to-day, but the Queen decided not to.
It's actually not all that common throughout history, but has become more common in the last couple of centuries for a variety of reasons. I think that Charles will be Charles III because the name has been so much a part of his identity for so long. His likely short reign would be swallowed up in a plethora of Georges otherwise.
Of course, he doesn't have to even use one of his names; technically speaking, he could use any name.
Also, Victoria's first name was Alexandrina, but she was known as Princess Victoria of Kent before her accession so she didn't really choose a different regnal name than the one she was known by.