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.

As others have mentioned, if the competitor is bidding on your client's brand name then it may fall under Google's trademark policy and you can file a complaint with Google.

If they're bidding on generic keywords however then the only thing to do is ensure that your quality score is as high as possible, which will reduce your ad cost and push you above your competitor whilst costing you less per click.

Most of the copycats that I've come across aren't very good when it comes to campaign optimization, meaning that most of the times it's fairly easy to achieve a much higher quality score than they'll ever see.

Make sure that your ad copy matches your keywords, that your ad copy + keywords match the content on your site, that you're linking people to pages that have good content (as opposed to "naked" landing pages), and you'll outrank your competitors shortly.

Hello,
maybe something not yet mentioned is to actually protect your brand by registering it (through your national registering agency, OHIM or WIPO, as examples).
You should know if your brand should be registered by calculating the profit driven by brand traffic vs registration costs.
Sure, advertisers will always be able to bid on your brand, but as you register it (first) and let Google know you want it to be restricted (second) you will succeed in having many advertisers using your brand in their ads, to have their ads disapproved.
They might then change the ads, but won't be able to mention your brand in their text ad anymore, hence become a worst Quality Score. With a worst QS it will be less profitable for them to keep bidding on your brand intensively.
I have successfully implemented brand defence strategies for my customers, increasing profitability on both paid and organic channels.

It has always been an unwritten Google Best Practice to bid on your competitor's brand names unless it is trademarked, Google does forbid having a competitor's name in your AdWords ad,

Online reputation management is an ongoing process that business owners often forget about. It is a challenge, but there are a few steps you should be taking on a regular basis. When your reputation suffers, the future of your business stands on shaky ground, so invest time into your online reputation management.
1. Social Listening: You need to have eyes and ears everywhere. Prevention is better than cure, so make use of social listening tools to track brand mentions as they happen. That way, you can monitor any suspicious social media accounts or activity and react before it is too late.
Some of these tools give you the option to get alerts as your brand is mentioned. And, while brandjacking is something that is more destructive to larger, corporate brands, it is something that businesses of all sizes need to be aware of.
Some free social monitoring tools to try including Hootsuite, TweetReach, Klout, Buzzsumo and Boardreader.
2. Crisis Response Strategy: Plan for the worst. Put procedures in place that will dictate how you react should a brand hijacking emergency occur.
Jay Baer created an “Internal Alert and Response Flowchart”. It basically specifies who should respond to a social media crisis. The more serious the issue, the more senior the responder should be:
Stage 1: Customer service team responds.
Stage 2: Customer service responds with management guidance.
Stage 3: Manager gets directly involved. Create content if necessary. Continue monitoring
Stage 4: Manager responds. Notify executive team. Create content. Continue monitoring.
Stage 5: Executive team responds. Create multiple pieces of content. Heavy monitoring.
3. Set up Social Media Accounts: Set up accounts on all social media platforms, even if you do not intend to use a certain platform at the time. If you’ve got all bases covered, there is less room for a hijacker to impersonate your brand, because most users should know which is the official one.
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath