The legal term for a false statement that harms someone’s reputation is defamation.
Defamation is an untrue factual assertion communicated to at least one other person that damages the subject’s reputation. In the United States, a plaintiff commonly must establish a defamatory statement, publication to a third party, fault by the speaker, and reputational harm, although the exact requirements vary by jurisdiction and by the plaintiff’s status.
Written or fixed defamation is traditionally called libel; spoken defamation is called slander. The distinction is useful, but modern laws and court procedures do not always treat the two forms identically. Opinions, rhetorical exaggeration, and substantially true statements generally receive different treatment from provably false factual claims.
Some statements are considered defamation per se because their subject matter is especially damaging, such as false accusations of serious crimes or professional incompetence. Public officials and public figures usually face a higher burden: under the US Supreme Court’s 1964 decision in New York Times Co. v. Sullivan, they generally must prove “actual malice,” meaning knowledge of falsity or reckless disregard for truth.