Antonyms for the phrase "lend one's name to" could include "disavow," "renounce," "reject," or "deny." These words suggest an unwillingness to associate oneself with a particular cause or activity. Conversely, antonyms might also include "champion," "endorse," "support," or "promote," which indicate a willingness to publicly lend one's reputation to a particular endeavor. Context is key when determining the most appropriate antonym, as a person or organization may choose to distance themselves from one aspect while simultaneously endorsing or promoting another. Ultimately, choosing the right antonym for "lend one's name to" requires an understanding of the nuances of the language and the thoughts and intentions of the person in question.