I have worked with a client with a similar issue. Their competitor was bidding on the brand name of my client. You will have to donate some Adwords spent and create “branded campaign” where you focus on bidding on your client’s business name. Your client should have a high quality score for their brand keywords since their website should but an authority on the brand name.

As far as stopping a competitor from bidding on the name the most you can do is send a cease and desist letter and I would only recommend this if the brand name has a registered trademark.