Although it can be a valid strategy to advertise for your own brand name using Google AdWords (and potentially for your competitors’ brand names), many people don’t look to see if there is actually anybody competing for those keywords.
If you rank number one for your brand name (which in most cases you ought to) and there is nobody else advertising for it, then putting up a paid ad above your organic listing is just burning money. See the example search results below; for a national business I wonder how much money they are wasting in clicks via Google AdWords that would have come naturally for free anyway?
This doesn’t just apply to your brand name however. If you rank number one for any keyword search organically and nobody is competing in the AdWords field for that keyword then you’ve got to have a very good reason to advertise against yourself (there are indeed some niche circumstances when you might consider this).
Check your keyword competitors, save yourself some money and stop competing against yourself!