The adjective eponymous traditionally describes someone for whom something, especially a work of art, is named. So, for example, the novel Jane Eyre‘s eponymous character is Jane Eyre, and the eponymous hero of the film Spartacus is Spartacus. In recent usage, however, the word is more often used to describe the work that is named after someone. For example, we might describe the album titled The Beatles as the Beatles’ eponymous album.
Neither sense is more right or wrong. The older sense is more in keeping with the word’s Greek origins, but etymology doesn’t guide real-world usage. And one point in favor of the newer sense of eponymous is the fact that eponym, the word’s root, indisputably refers to something, especially a word, named after a person. Eponym does bear an older definition corresponding to the old use of eponymous, but it’s seldom used in that sense.
Similar issues surround namesake, which is also used in contradictory ways. It means both one for whom someone is named and one who is named after someone.
These writers use eponymous in the old way, to describe a person after whom something is named:
There is a scene in Monty Python’s Life of Brian in which the eponymous hero wakes up to find his home surrounded by disciples. [Irish Times]
Shem, the eldest son, is the eponymous ancestor of the Semites, including the Jews, Arabs, Assyrians, Elamites, and Aramaeans—but not the Canaanites. [What Are the Seven Wonders of the Word?, Peter D'Epiro and Mary Desmond Pinkowish]
In “Cyrus,” his eponymous character is both villainous and pitiable. [Salon]
And these writers use eponymous in the newer way, to describe something that is named after someone:
Kottke launched his eponymous site in 1998, back when blogging was just getting started. [Slate]
Bacharach’s eponymous album came on the heels of two Top 10 hits. [Burt Bacharach, Song by Song, Serene Dominic]
All the fashion hits are there; the sequinned dress from Tom Ford’s triumphant eponymous collection. [Telegraph]