Your brand or your business is often searched online by both potential and existing customers. Even though you may expect (and want) customers to just visit your business directly if they know your name, the overwhelming chances are they are still searching for your business name in Google, why, because that is easier for them!
That means it's another opportunity to win (or lose) a customer - I know it sounds crazy, they are already searching for your business, why advertise to them?
But really, the battle is never over - and there are important reasons you will want to consider running ads on "branded" search terms.
Competitors - defend your potential customers from competitors who may be bidding on your business name or branded terms. Though the searcher may be looking for you, a well-timed ad from a competitor may be enough to convince them away from your business and go somewhere else, making sure you're above their ad can be crucial in capturing important, qualified visitors.
Dominate the page - Although your site may appear in the organic listings, having an extra ad above means that your business takes over the whole page, improving the user perception of your business and giving you more opportunity to win the customer.
Better messaging - A free listing is great but an ad gives you extra ability to customise and improve your messaging to the user. Call out things like offers, special features, or benefits, and you'll have a better chance of a happy, returning customer.