They say that when you're famous you lose the given name, when you're more famous it's the only name you go by. In this case is it maybe dependent on country?

They say that when you're famous you lose the given name, when you're more famous it's the only name you go by. In this case is it maybe dependent on country? I know that he was Da Vinci, but always heard mostly "Leonardo" alone. (also Miguel Ángel y Rafael) People saying that "Da Vinci" only means he was from Vinci, come on, that's the case for a lot of family names and it's because, you know, people that started with such name came from such place.