I asked this a while ago but I'm not sure what the answer is. I think that anyone who becomes a king or emperor is generally known by their first name, hence Napoleon rather than Bonaparte. But this doesn't explain Michelangelo, Dante etc. In particular it doesn't explain why we talk about "Michelangelo" but "Botticelli". Are we just more pally with Michelangelo?
Giving a list of people from the Bible is pretty pointless (even if you spell them all correctly) because all those characters only have one name anyway, even the ones that were historical (such as Jesus) as opposed to the mythological ones (such as Cain and Abel - and how many mythological characters have more than one name anyway?). Such people would be "surnamed" either by their place of origin (eg Jesus of Nazareth) or by their father (eg James and John, the sons of Zebedee). Jesus might also have been known as Yeshua Bar Yoseph, that is, Jesus son of Joseph (I have encountered educated people who genuinely believed that "Christ" was Jesus' surname, but I'm sure that no-one here is daft enough to think that!). Michael is an angel, so I don't know why he's been mentioned.
Also, note that "Plato" was a nickname. His real name isn't known.
The lack of a surname goes for most ancient western people, which is why everyone in antiquity and the early Middle Ages is called so and so of such and such a place (Basil of Ancyra, Gregory of Nazianzus, etc). So there's not much point asking why such people aren't referred to by their surnames, as they didn't have any. Some names that we think of as surnames were actually nicknames - for example, "Abelard" - which is why it's interesting that we always call him "Abelard" as if it's a surname, rather than "Peter". The same goes for "Aquinas", which simply refers to his place of origin.
So the question only really applies to modern people, such as the artists mentioned.