An eponym is a person for whom a place or thing is named, or believed to be named, or the name itself. For example, Léon Theremin is the eponym of the theremin, an electronic musical instrument.
The derivative adjectives eponymous and eponymic refer to the person or thing for whom a place or thing is named, as in "the eponymous founder of the Ford Motor Company". Recent usage, especially in the recorded-music industry, also allows eponymous to mean "named for its creator or central character".
In Ancient Rome, one of the two formal ways of indicating a year was to cite the two annual consuls who served in that year. For example, the year we know as 59 BC would have been described as "the consulship of Marcus Calpurnius Bibulus and Gaius Julius Caesar" (although that specific year was known jocularly as "the consulship of Julius and Caesar" because of the insignificance of Caesar's counterpart). Under the empire, the consuls would change as often as every two months, but only the two consuls at the beginning of the year would lend their names to that year.
During the Christian era, many royal households used eponymous dating by regnal years. The Roman Catholic Church, however, eventually used the Anno Domini dating scheme based on the birth of Christ on both the general public and royalty. The regnal year standard is still used with respect to statutes and law reports published in some parts of the United Kingdom and in some Commonwealth countries (England abandoned this practice in 1963): a statute signed into law in Canada between February 6, 1994 and February 5, 1995 would be dated 43 Elizabeth II, for instance.
Both in ancient Greece and independently among the Hebrews, tribes often took the name of a legendary leader (as Achaeus for Achaeans, or Dorus for Dorians). The eponym gave apparent meaning to the mysterious names of tribes, and sometimes, as in the Sons of Noah, provided a primitive attempt at ethnology as well, in the genealogical relationships of eponymous originators.
Because proper nouns are capitalized in English, the usual default for eponyms is to capitalize the eponymous part of a term. The common-noun part is not capitalized (unless it is part of a title or it is the first word in a sentence). For example, in Parkinson disease (named after James Parkinson), Parkinson is capitalized, but disease is not. In addition, the adjectival form, where one exists, is usually lowercased (thus parkinsonian although Parkinson disease and gram-positive although Gram staining).
However, some eponymous adjectives and noun adjuncts are nowadays entered in many dictionaries as lowercase when they have evolved a common status, no longer deriving their meaning from the proper-noun origin. For example, Herculean when referring to Hercules himself, but often herculean when referring to the figurative, generalized extension sense; and quixotic and diesel engine [lowercase only]. For any given term, one dictionary may enter only lowercase or only cap, whereas other dictionaries may recognize the capitalized version as a variant, either equally common as, or less common than, the first-listed styling (marked with labels such as "or", "also", "often", or "sometimes"). The Chicago Manual of Style, in its section "Words derived from proper names", gives some examples of both lowercase and capitalized stylings, including a few terms styled both ways, and says, "Authors and editors must decide for themselves, but whatever choice is made should be followed consistently throughout a work."
English can use either genitive case or attributive position to indicate the adjectival nature of the eponymous part of the term. (In other words, that part may be either possessive or nonpossessive.) Thus Parkinson's disease and Parkinson disease are both acceptable. Medical dictionaries have been shifting toward nonpossessive styling in recent decades. Thus Parkinson disease is more likely to be used in the latest medical literature (especially in postprints) than is Parkinson's disease.
National varieties of English
American and British English spelling differences can occasionally apply to eponyms. For example, American style would typically be cesarean section, whereas British style would typically be caesarean section (or cæsarean section [with digraph]).
Comparison table of eponym orthographic styling