It comes down to why he's known as Napoleon instead of Bonaparte, he was an Emperor. Louis, Henri, Frederick, the first names of Kings from various houses, Napoleon aimed to create the House of Bonaparte, named his son Napoleon whom is known as Napoleon II. So it basically goes to the naming convention of dynastic relations.

Because he's Emperor Napoleon the First. However, in France, when speaking of him before he became emperor, he is still referred to as Bonaparte. Also, when he signed his name, he signed it Bonaparte or Napoleon Bonaparte or Napoleon Buonaparte before he became emperor, then afterwards he signed it simply Napoleon.

Every other conquerer and world leader in history, it seems to me, is referred to by last name.

Alexander the Great is referred by his name Alexander, Darius I is referred to by his name Darius, Gaius Julius Caesar is commonly referred to by his cognomen Caesar, Temujin is commonly referred to by his title Genghis Khan. Just some examples.

Its actually, contrary to the question, fairly rare for kings and emperors to be known by their second name. This is because before the modern era, we didn't really have 'second names' but Houses. (It was actually fairly rare in a lot of places for commoners to have a second name, and it only became a legal requirement in the Netherlands in the early 19th century!)

Because, hopefully, the next king after you would be of your house, if everyone was known by their second name, the names would be the same every time. That would get pretty confusing. (I say that, but France had like 17 kings called Louis, and 80% of Bourbon monarchs were called Louis, so maybe they weren't as fussed about it over in France.)

Napoléon's baptism record mentioned Napoleone di Buonaparte. Which is his baptism name. On the record of his wedding to Josephine, he signed Napoleone Buonaparte.

Also, Napoléon was always quick to write. He never really learned to write properly in any language and always signed by the first thing to come into his mind, until he was more careful to sign Napoléon.

I just want to mention that Napoléon's French was catastrophic ( which was the same for most French people actually at his time, except for the inhabitants of the Ile de France region ( Paris and the surroundings ) until after WW1. People spoke local/regional dialects.

There are plenty of rulers known by their first name, common in dynasties: William the conqueror or the 1st Pretty much ecery other monarch Alexander the Great A couple of examples come to mind

Alexander, Nefertiti.... I am not a history buff and there are two so it would seem your question is flawed on that there are probably many