On ADS-L on the 27th, Victor Steinbok noted the rarity of the useful adjective mononymous (and nouns mononym and mononymy) — cf. homonymous, synonymous, antonymous, etc. From Paul McFedries’s WordSpy entry (posted 7/18/98):
adj. Describes a person who uses only one name. [or the name itself -- AMZ]
Example Citation: ”The mononymous Cafu is a defender for Brazil, the world’s most stylish and self-absorbed collection of athletes, a team aptly described by one Brazilian newspaper as a ‘cauldron of vanities.’ ” —Steve Rushin, “Tour de France,” Sports Illustrated
For example, Socrates, Cher, Banksy, Pelé, Batman, to choose people from various walks of life.
The Rushin cite is the only one Victor found in dictionaries for the word. The alternative McFedries suggests, uninomial, seems not to be any more frequent than mononymous (with reference to personal names, that is; see below). Other alternatives are longer but less technical-sounding (e.g., “a philosopher with a one-word name” instead of “a mononymous philosopher”).
For whatever reason, the technical vocabulary seems not to have caught on, even though it would sometimes be useful to have such a brief (mononymous!) term. But of course nothing obliges speakers to opt for brevity, against other considerations (like the naturalness of ordinary vocabulary).