Used when something is named after a person, often its creator or someone it's dedicated to. The Ford car company is eponymous, named after its founder Henry Ford.
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Cultural Usage
Often used in arts and entertainment to indicate works named after a central character or theme. Shakespeare's 'Othello' is the play's eponymous protagonist.
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Avoid Confusion
Don't confuse 'eponymous' with 'anonymous'; 'eponymous' always indicates a known name. Unlike an anonymous donor, the eponymous sponsor of the event was well-known.