Even though Joan Jett sang about not minding her bad reputation, most of us don't want others to defame us. To defame is to gossip, even if the story is made-up, with the goal of hurting someone's image.
We usually think of fame as a positive thing. Love, admiration, and people wanting to be like you — it all comes with the territory. The de- in defame means "remove." So if someone tries to defame a person, fame — or a good reputation — is taken away. Celebrities protect themselves from those who want to defame them, arming themselves with lawyers.