Reputation risk is a second order risk. It is caused by some other risk event. Coke cannot go out and buy some reputation risk insurance but it can try to ensure that it’s factories don’t stop working or rat droppings don’t show up in its beverages. These can be treated or controlled. It is only when the first order risks fail will Coke suffer from a risk event to it’s reputation.
The best an organization can do is ensure that after an event it has an effective communication strategy in place to minimize the negative effects to its reputation and get its customers back.
Summary: Reputation = second order risk. So stop wasting time and putting it on your risk profiles as if you can do something about it. Focus on the risks which you can actual treat.