One task I had to recently complete was cleaning up the Facebook ecosystem for a particular business. Around Facebook there were a few groups, profiles and pages purporting to be the business which needed removing. There are two types of infringement that you can report to Facebook and get actioned, explained below.
For copyrighted works, such as music, movies or images you can have them removed via the Facebook automated DCMA removal form.
If you are the legitimate representative of a business you can ask Facebook to remove any unofficial pages, groups or profiles which are purporting to be you. You need to complete the Facebook non-copyright removal form.