Laws and rules for private process servers?

I have this guy who has been harassing my grandmother and me for over a month know. He keeps going to my grandmother's house even though she has told him I do not live here. He has left rude and threatening messages on my phone (even telling me that I was irresponsible!) He said he is a private process server and I HAVE to give him my information (which I have refused to contact him back because I have no idea who he is). He only gives a first name and a FALSE business name(he uses more than one from what I've read online from others who have been contacted by him). He said over two weeks ago that he was just going to turn the papers over to the sheriff's department(which is fine with me because I will deal with them because I KNOW they are legitimate and do things legally) However he since then has continued to show up at my grandmother's house and call me. He even tried to make my grandmother believe he was with the sheriff dept the first time he showed up!! He says he is going to show up at my work (which is fine because he had old work information). He said it's regarding an "unpaid medical bill" however BOTH medical institutes in town have my currently physical address (not my grandmothers) to contact me at. I have already contact the Clerk of the District court who has said that there were no current papers filed against me. So I have since forwarded this whole situation to the local authorities to see what we can do regarding his harassment's (and threatening demeanor) but they have yet fully open it into a case. I just want to know legally what this guy as a private process server (if he really is one) can do and say to me and my grandmother.