Ive recently performed an extensive search for a particular business name and was allowed to register my name in the state of arizona. I just found a person using that name on a facebook page. He has not registered and is operating without a license or tax id. Or ROC license. It seems that it is a very inactive business and does not appear anywhere else in any media or on the web. Can he come back and claim that name after ive registered and servicemarked it?