Your Google Ads never show up on terms unless you bid on those terms. So by default, your ads won't show up for your branded searches. To get your ads to show up for your brand name you would actually have to bid on your own brand name. It is very common practice to do so.
You can usually get the clicks on your brand terms cheaply; often 1 or 2 cents per click. That is because your quality score will be very high for these ads. You use your unique brand terms in your pages and users find your ads highly relevant and click on them often.
Bidding on your own brand terms pushes your competitors out. Your competitors may have to pay 20 or 30 cents for the same click that you get for a penny. Their quality score will be much lower because of lower interest and inability to use the trademarked terms on their pages.
Some studies have shown that having a paid ad plus an organic listing leads to more clicks to your site for brand searches than if you had only the organic listing.
For more reasons why bidding on your own brand is a good idea and usually done, see this article on Search Engine Journal: 13 Reasons Why PPC Brand Bidding Is a No-Brainer
