Whatever you may think of the British monarchy, Queen Elizabeth II didn't make it that way and it was not in her power to change it fundamentally. All she could do was be the best Queen she could, and I think she did pretty well: presiding, not ruling, and doing it with dignity and not behaving as if it was a total waste of her time.
Seventy years of it. And she was on the job to the end, commissioning a new prime minister only two days ago. (That makes 15 different ones in her reign, 3 of them women.) She was 96. Some were expecting her to go on a lot longer: her mother lived to be 101.
And now, King Charles III. Some wondered if he'd take that name. After all, the first two Charleses were hardly ideal models of royalty, and the name "Charles III" already had a smudge on it, being the term the Jacobites used for Bonnie Prince Charlie after his father, the Old Pretender, died.
But it's usual for the monarch to take his or her own name. Some articles have implied it's not, but the circumstances in which a king took a different name were rare and unusual. (In both cases it was a prince named Albert, due to Victoria's attempt to honor her husband. Both thought a King Albert was inappropriate, and took a middle name instead. Also, Victoria was actually her middle name (her first was Alexandrina), but she'd been called Victoria from childhood.
When Elizabeth became Queen, some expected her to take another name. There'd been only one Queen Elizabeth; was there the nerve to change that? But the Queen said it was her name and she was keeping it, and it turned out not to be much trouble to refer to the earlier monarch as Elizabeth I.
The official accession is a meeting of the Privy Council, probably tomorrow. The coronation comes later. It's a big ceremony but it doesn't mark the beginning of the reign. The Privy Council does that. By the way, I'd like to inform the radio announcer who was blabbing about it that the verb form of what the monarch gets at the coronation isn't "coronated." It's "crowned."
The Duke of Cambridge is now also Duke of Cornwall. That's automatic. But he doesn't get to be Prince of Wales unless and until the monarch says so. Elizabeth waited several years before giving that title to the (admittedly then very young) Charles.