Recently (in no small part to EconTalk's new book club starting with the Theory of Moral Sentiments) I've been given thought to if people should speak bad of others and if a person owns their reputation. The impulse seems to be that of course they do. It is their reputation, isn't it? Do they not have a right to know if someone speaks ill of them and to prevent harm to their reputation?
But calling it "my" or "her" or "their" reputation is really a semantic shorthand, much like "my" job or "my" girlfriend. We do not say it to convey possession, but rather relation. It is fundamentally not the same thing as my book, my computer, or my wallet.
The fact that a person's reputation can be harmed (and thus the person herself) should not be considered, either. A firm can (and is) harmed by their competition, but no one says McDonald's owns Burger King. Similarly, a critic who gives a negative review of a movie is thus not controlled by the movie's studio. Just because something can harm you, doesn't mean you own it.
Your reputation is the sum of what others think about you. To say you own your reputation is to say you own others' thoughts which is clearly nonsense. You don't own your reputation. Others do.
This is not a green light to spread lies. Lying is a violation of implicit contract between the listener and the talker--regardless of if a reputation is actually harmed (I'm told many things about many people I don't believe). But if reputation is harmed through expression of fact (including opinion presented as opinion), it's hard to claim the subject of conversation has a case of being wronged.
Smith advocated against harming another's reputation but has a valid function. People get bad reputations for reasons, most of which are justified. Spreading opinions can prevent disasters for others later (again, assuming there are no lies involved). Far from being malicious, speaking bad of someone actually helps people.