Discuss the matter with an intellectual property (IP) attorney--if you have been using the second name in commerce (i.e. operating under it,  providing services under it, etc.), you may be able  to protect it as a trademark/service mark or tradename. That is, you may be able to assert your right, based on your use, to the name; send a cease-and-desist letter to the other person or group; file a legal action against them, for infringement or unfair competition, if they don't desist; and also register the name for greater protection in the future.  Much depends on the specific facts, including, most importantly, whether you have been using the name before this other person or group started using it--primacy or priority of use is very important in this area. You need experienced IP counsel to evaluate the situation for you, so you understand your rights and options.