It’s been my understanding (in Renaissance art history, anyway) that in 15th century Florence (and most other places in Italy), surnames were fashionable for noble families (or family houses that aspired to nobility)–most artists were from working class families, and thus generally didn’t have surnames. Patronymics were used simply to distinguish individuals with the same Christian name, although certain individuals became so famous that patronymics aren’t needed.
So, to keep with the theme of famous Renaissance artists/Ninja Turtles, we speak of Raphael, Michelangelo, and Donatello, rather than (respectively) of “Sanzio,” “Buonarroti,” and “di Niccolo di Betto Bardi.” The same convention is applied to Leonardo da Vinci, whom (in art history, anyway) is referred to simply as “Leonardo.” I can’t really think of any other Renaissance artists named “Leonardo,” so there’s little risk of confusion if one leaves out the patronymic of “da Vinci” (though there was also an artist named “Pierino da Vinci,” who was actually the nephew of Leonardo… but I digress).
However, this usage (of calling an individual by their Christian name alone) is based on 15th-16th century Italian conventions, which weren’t always consistent. “Michelangelo” as a name and a person is an interesting example of this inconsistency. THE Michelangelo–the guy who painted the Sistine Chapel ceiling, of course–was unlike most of his artistic peers in the fact that he could claim noble ancestry, so you could make a case for calling him “Buonarotti” as a surname, instead of simply “Michelangelo.” But by convention, he became known as just “Michelangelo,” of such fame that no patronymic or (in his case) surname was needed to distinguish him from anyone else named Michelangelo.
Funny thing is, by the end of the sixteenth century, another artist called Michelangelo became active in Rome–his name was Michelangelo Merisi (like Michelangelo Buonarroti, this Michelangelo came from a family that claimed descent from lower nobility). However, the Romans didn’t call this artist “Merisi,” nor could they bring themselves to call him “Michelangelo” (and risk conflating him with the established legacy of the most famous artist by that name). So, Michelangelo Merisi became known by the nickname “Caravaggio,” referring to the northern Italian town that his family called home. In the case of Caravaggio, then, the patronymic (“from the town of Caravaggio”) is used instead of the Christian name “Michelangelo” or the surname “Merisi.”
I’m not sure if this clears anything up.
