An eponym is a person, place, or thing after whom or after which something is named, or believed to be named. The adjectives derived from eponym include eponymous and eponymic. For example, Elizabeth I of England is the eponym of the Elizabethan era, and "the eponymous founder of the Ford Motor Company" refers to Henry Ford. Recent usage, especially in the recorded-music industry, also allows eponymous to mean "named after its central character or creator".
The Hebrew Bible explains the origins of peoples through individuals who bear their name. Jacob is renamed "Israel" (Gen 35:9) and his sons (or grandsons) name the original 12 tribes of Israel, while Edomites (Gen. 25:30), Moabites and Ammonites (Gen. 19:30-38), Canaanites (Gen. 9:20-27) and other tribes (the Kenites named after Cain Gen. 4:1-16) are said to be named for other primal ancestors bearing their name. In most cases, the experiences and behavior of the ancestor is meant to indicate the characteristics of the people who take their name.
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, itself eponymous, 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. 
Government administrations may become referred to eponymously, such as Kennedy's Camelot and the Nixon Era.
Plays, books, and other forms of entertainment may have eponymous names, such as the ancient Greek epic The Odyssey, derived from its principal character, Odysseus, and the novel Robinson Crusoe.
The term is also applied to music, usually with regard to record titles, where it is prevalent and leads to confusion. For example, Bad Company's first album was entitled Bad Company and contained a popular song named "Bad Company". Parodying this, the band R.E.M. titled a 1988 compilation album Eponymous.
In tribal antiquity, 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.
In zoology, an animal name that includes the name of a person is properly called an eponym.
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."
When the eponym is used together with a noun, 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 for medical terms (thus parkinsonian although Parkinson disease), and gram-negative, gram-positive although Gram stain. Uppercase Gram-positive or Gram-negative however are also commonly used in scientific journal articles and publications. In other fields, the eponym derivative is commonly capitalized, for example, Newtonian in physics, and Platonic in philosophy (however, use lowercase platonic when describing love). The capitalization is retained after a prefix and hyphen, e.g. non-Newtonian.
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 non-possessive.) 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 may apply to eponyms. For example, British style would typically be caesarean section, which is also found in American medical publications, but cæsarean section (with a digraph) is sometimes seen in (mostly older) British writing, and cesarean is preferred by American dictionaries and some American medical works.