@Highskirt There's no question of "Appointment" to it! Charles' Eldest child, William, becomes the Sovereign automaticly upon his death, but he may abdicate sooner of course, whereas Prince William would also then become King.
King 👑 Charles is 73 right now, Prince William is now 40. So, perhaps after 10 to 12 years of Reign as King Charles might well Step Down / Abdicate the Throne of England and hand it over to his Son. He's been a Prince for his entire 73 years! Maybe he won't take well to the Role of King or England?
In a statement attributed to His Majesty The King, Charles writes:
"The death of my beloved Mother, Her Majesty The Queen, is a moment of the greatest sadness for me and all members of my family.
We mourn profoundly the passing of a cherished Sovereign and a much-loved Mother. I know her loss will be deeply felt throughout the country, the Realms and the Commonwealth, and by countless people around the world.
During this period of mourning and change, my family and I will be comforted and sustained by our knowledge of the respect and deep affection in which The Queen was so widely held."
@Incomplet Yes... He COULD choose whatever name he wants - in theory.
In practice, that's not a very good idea because the country may then take steps to remove King Snooty Gizzard VII from the job in light of him being unfit for the job.
That was a danger for the late Queen in the last years of her life.
As far as not telling anyone other than the Archbishop of Canterbury goes... that is incorrect. His Majesty has to tell the government who they are serving which is where King Snooty Gizzard VII could meet a swift end since it is in Parliament where the motion to remove him from his new job can be tabled.
Further to that, in the next couple of years or so, new currency will be released into circulation, bearing his name. Anything much longer than "Elizabeth" or "William" will be too long on smaller coins and won't fit alongside the details already there and the new letters that the King has inherited.
There are reasons why the monarchy chooses to reign using "old fashioned" names. It's more trouble than it's worth to try and bring in a name like "King Ronald I".
The coronation usually takes place several months after the death of the previous monarch, as it is considered a joyous occasion that would be inappropriate while mourning continues.
So there's Absolutely No Big Hurry at All!
A coronation is a symbolic formality and does not signify the official beginning of the monarch's reign; de jure and de facto his or her reign commences from the moment the preceding monarch dies, maintaining the legal continuity of the monarchy.