There are no rules against bidding on a competitor’s brand name via Google Search, but you can’t use their name in your ad if it’s trademarked. The Google quality score system means bidding on a competitor name is often pricey because you can’t be relevant to the keyword. So the best way to stop a competitor bidding on your name is to bid on your own brand name and push them out of the auction. You’ll always be most relevant to that keyword and pay a fairly low cost per click.