I had those same obstacles in the search for my bio father. And, the majority of the matches who responded to my messages were adoptees, so searching, too. So many unknowns. On top of that, my two highest non-maternal matches were already dead. In addition to that, my mother is in denial and stopped speaking to me over this.
In spite of(or maybe to spite!) those obstacles, after about 8 months I had found my bio grandparents. They had three sons to choose from. I was finally able to get one to respond and agree to test. He came back as my uncle. He asked brother #2 to test. After 16 months, I finally confirmed my bio father.
You don’t need their name in order to start the process. The DNA matches will ultimately expose it.
I am no expert by any stretch, I was desperate and learned as much as I could about building out the available match trees and match charting methods. Also, search Google for the screen names your matches are using. Sometimes people use the same screen name across different sites. Facebook sleuthing can be helpful, too.
I can try to help you, if you want help and haven’t accepted any of the other offers. Message me and I will send you my email address.
Best wishes to you in your search. I know how overwhelming it can be. I have been there.
Have a blessed day.
Your sis in Christ,