I’d like to talk frankly about a real threat to the British monarchy.
First, monarchs like to emphasize continuity and tradition by reusing names from previous monarchs. This is understandable as, in a constitutional monarchy, continuity and tradition are the monarchy's main assets. Perhaps for this reason, a British king hasn’t taken on a previously unused name since George I in 1714.
However, this bumps up against a contradictory historical tendency, namely that British monarchs have had what might be described as a rich and varied history. British kings aren’t eager to remind people of their more colourful predecessors. Many names are therefore out of bounds.
The result is that the British monarchy is rapidly running out of names in the male line. For example:
Henry — It is difficult to imagine the king who would want to be Henry IX, and even more difficult to imagine the woman who would want to marry him.
Richard — Who wants to be the successor of the King in the Car Park? And there was the business with the Princes in the Tower.
Edward — Although the abdication of Edward VIII might be viewed more romantically by modern eyes, the Nazi sympathies, not so much.
John — The Magna Carta was written to protect people from him.
James is right out.
Once you factor in this history, there are very few names left. Charles is still OK. Charles II granted the charter of the Royal Society; perhaps a future Charles III could also take an interest in science. William and George are unimpeachable. Albert is a possibility, although the famous Albert was only a consort, making the name a bit of a risk: the last prospective King Albert decided at the crucial moment to become a George instead.
This is shaping into a crisis. One can imagine a time, in the coming centuries, when the only choices left to British kings are Charles, George, and Cnut.