Competitor is ranking for my Brand name, What can I do?
Here is the guaranteed process to remove someone ranking for your brand name on Google search results:
You can complain to Google if a page appearing in Google’s search results is violating your company’s trademark rights. But they will suggest you to contact the webmaster. So the best way to go is get a court order declaring your business rights and order to remove unlawful contents from search result page (e.g. pursuant to a copyright or trademark infringement suit). You can find more information here: http://support.google.com/legal/answer/3110420?hl=en
An excellent guide to the whole process: http://www.defamationremovalattorneysblog.com/2014/12/how-to-remove-urls-from-google-after-obtaining-a-court-order
The next step would be creating web presence of your website to climb in ranking which you can do by creating social profiles of your brand name with your official website. You may do this at top 50 social media sites including Google+. Here is a simple plan: 1. Create social profiles and update existing ones 2. Interlink all the profiles and link to your website 3. Fill all the profiles with some good amount of posts 4. Build 200-300 1st and 2nd tier backlinks to the profiles and your official website
If you are not sure how to get a court order, you can get help from a professional finding a lawyer. After you get the court order submit it to Google.
Make sure you create all the social media profiles of your brand name with official website. To be honest, just by creating the social profiles may push you up in ranking for your brand name and drop the current page ranking on 1st place. But the court order will legally do the job for you.