It’s cool that the King/Queen of England can choose a new name for themselves. The Pope also gets to change his name to a name that comes from a prior pope, or in the case of Francis he used Francis for the first time.
I believe a name carries some weight. It becomes your promise, trademark, and statement.
With all this being said, I like my name. It’s not all that common. Now if I were to change it I would like the name Peter. In the Bible, Peter is given the task of building the church and is considered to be the first Pope. Peter is derived from the word “Rock” not that I am a rock or anything like that, but I am a solid guy I think.