The Telegraph has
an article about how little George might change his name upon accession because a lot of other Kings have done so. Personally I kinda feel like HM on this issue. Little George will presumably be called George by friends and family, and will be known as Prince George, so why would he choose to go by Alexander all of a sudden when he becomes King? I can understand why George VI decided to reign as George instead of Albert, because he wanted to honour his father and I would be understanding if little Estelle in Sweden chose to go by Mary instead of Estelle because, unlike little George, she has a name that's less traditional. I don't know, I just think it's weird, I would personally feel very weird about one day just scrapping a name I've gone by for all of my life, in favour of one of my secondary names.
Lou-ee, not Lewis (due to contrary belief - I've heard so many people pronounce it like that and I just wanna shake them and shout "LOU-EEEEEE!!!" because it really bothers me).
Edward VII - he was baptised Albert Edward and the expectation was that he would reign as Albert Edward I but he decided to just use Edward and reigned as Edward VII.
As far as I am aware they are the only three - Victoria, Edward VII and George VI - but they have all been in recent years so it has become a bit more of a tradition with 3 of the last 6 opting for a different regnal name to their baptismal name.
I think the idea in the Telegraph is that "a lot" of monarchs in Europe have done the name change, but they kind of miss the point that not a lot of English/Scottish/British monarchs have done it.
No English monarch ever changed their name and, to the best of my knowledge, only one Scottish monarch did so - Robert II was initially named John.
Three British monarchs, and one consort, have change their names - Victoria, Edward VII, George VI, and Mary, but none of them did so lightly or without reason.
Victoria was known by the public as Princess Victoria so it was only natural that she would go by that during her reign - although initially it was expected that she would use Alexandrina Victoria.
Edward was Albert Edward, with the expectation that he would reign using both (and that every monarch after him would be Albert Something). He chose to drop part of his name, which shouldn't have surprised anyone given his relationship with his parents.
Mary was, prior to her marriage, known as Princess Victoria Mary, but always went by May. Victoria was dropped when she became Queen consort because they didn't want to have the double first name and so as to not diminish Queen Victoria.
George came to the throne in a period of instability and took a lot of measures to appear reassuring and like he was going to continue the stability of his father's reign. The name was just one factor in that.
It's unlikely that Charles, William, or Baby George will change their names when they come to rule. They all are (or will be) well known in the public by their first names, they all have British Royal names, none of them have a double name, and none is likely to come to the throne amidst the chaos similar to the abdication crisis.
The likelihood of someone coming to the throne and hanging their name is slim. In my opinion it's only likely to happen if some disaster happens and an individual with a really non-traditional name becomes the monarch. If Zara somehow came to the throne she might chose to reign as Anne or Elizabeth, but Baby George? Not likely.