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).
(Another mononymous cite that Victor found:
About a week ago, a group of Tumblr users, led by Raven, a mononymous Chicago-based progressive activist, began to tweet taunts, insults, and other expressions of outrage at Ryking, whose selections of political material on the service earned him the status of “tag editor” on the blogging service. (link))
There are cultures in which mononymy is commonplace, or even normative. In such contexts, it’s not worth commenting on. But in the many cultures in which dinymous names — a personal name plus a family name, in one order or the other – are the norm, mononyms stand out. In British and American usage, trinymous names (Franklin Delano Roosevelt, Arthur Conan Doyle, Edgar Allan Poe, etc.) also stand out if they are customarily given in full. So there are times when we want to talk about the number of words in expressions.
Finally, dinymous and trinymous seem to be even rarer than mononymous. Uninomial, binomial, and trinomial, on the other hand, are reasonably common, but not with reference to personal names; instead, they are used with reference to algebraic expressions and to taxonomic names in biology. In biological nomenclature, uninomials are used for names at or above the genus rank (the genus Canis). A specific name is binomial (the species of gray wolves Canis lupus), a subspecific name trinomial (the dingo Canis lupus dingo).
In both cases (algebra and biology), uninomial etc. are clearly technical terms, appropriate in their contexts; compare monosyllable, disyllable, trisyllable, etc.in discussions of phonology. For everyday purposes, things like the following (adapted from actual examples) are just fine, and a technical term would be just fancy overkill:
Name a band or singing group that goes by a one-word name.
What are good one-word names for a book?
What is the longest one-word name in the world?
I’m looking for movie with a one-word name; it starts with R, …