If the links in question are doing something illegal in connection with the product name, you can try to file a DMCA (Digital Millennium Copyright Act) report against the people who manage the URLs the links point to and/or file a lawsuit against them. Then again, it depends on how illegal the act is to begin with.
If you did invent the product name, it would be extremely helpful if you had a set of laws surrounding third-party usage of the product name or anything else related to the product so that you have something to back you up should someone use your product name in an illegal way.
I personally would find it silly if for example, you were selling a product and you wanted to remove the blog URL (that is listed before yours) that talks about how wonderful the same product is along with providing a link to your site. It's like asking to burn bridges.
If you do want to rank on top of the list, you should follow Google's Webmaster guidelines and write quality content.
Other than that, good luck.