Some people so completely own their first name or last name that their other name is more or less unused when describing them. For instance:
Napoleon (Bonaparte)
(Mohandas Karamchand) Gandhi
Naturally, some other names make it pretty easy to guess who you’re talking about, but they’re not quite one-namers. If I say Lincoln you’ll probably think of the 16th President of the United States, but he’s still generally know as “Abraham Lincoln,” not just “Lincoln.”
Who’re other good one-namers? (Note: Monarchs are cheating.)
Mozart
Beethoven
Handel
Mendelssohn
Schubert
Schumann
Wagner
Mahler
Berlioz, etc.
In fact, even when there is ambiguity, we still tend to use the last name only.
Bach could refer to Wilhelm Friedrich, Carl Phillip Emmanuel or Johann Christian Bach, but it is usually assumed that Johann Sebastian Bach is the one who is meant.
Haydn could be Michael Haydn, but usually refers to his more famous brother, Joseph Haydn.
Johann Strauss II and Richard Strauss are often referred to by their last names only, leaving the title of the work and the context to help you sort out which one is meant. ‘Blue Danube’, ‘Die Fledermaus’ - that’s Johann. ‘Also Sprach Zarathustra’, ‘Salome’, ‘Four Last Songs’ - that’s Richard.
In many places, as just Lincoln. I’d bet money that many people outside of the US would answer “name of the guy who was president of the US during their Civil War?” with just the lastname.
Plato, which has been mentioned several times, is actually a nickname. Most ancient Greek philosophers are known by a single name, as are most prominent Roman figures.
Of course – most of those single nsames aren’t the person’s real name in many of these cases, but a pseudonym, or nickname, or the name imposed on them by foreigners. “Stalin” is “Man of Steel”. “Lenin” is a pseudonym. “Saladin” is a foreign corruption of the real name, as is Darius, the originsal of which is the more authentic-psounding Daryavahush.