byword

A proverb or proverbial expression, common saying; a frequently used word or phrase.

A characteristic word or expression; a word or phrase associated with a person or group.

Someone or something that stands as an example (i.e. metonymically) for something else, by having some of that something's characteristic traits.

Illustrious unfortunates attract a wider sympathy, not because their griefs are more intense, but because, being set on lofty pedestals, they the better serve mankind as instances and bywords of calamity.

An object of notoriety or contempt, scorn or derision.

He hath made me also a byword of the people […]

"I know you and Harry are inseparable. Surely for that reason, if for none other, you should not have made his sister's name a by-word."

A nickname or epithet.