Do I pay taxes for both state?

I rent an apartment in PA but work remotely for TX. However, I do not file PA taxes. I still show myself as a TX resident and pay TX taxes. I have not changed my TX license to PA either. Is my employer still required to pay PA taxes? I'm not a contract worker. My employer is not registered with PA state. Their office is only in TX. My employer wants to avoid paying the extra fees that will cost them for an employing someone remoting into work. They asked me to get a d.b.a for a business so they can pay me as if they were paying a company. The business account under my dba will only be used to receive my paycheck and paying my personal bills. Can I get a dba only for these reasons? I will get the dba in Fort Bend County, TX and show that it is a home based business so that they can mail my checks to my mom's house.