I (24 trans man) am located in NJ. I was rejected and estranged by my bio family due to being transgender. I was "adopted" by someone who has been a father figure to me for a long time, as my bio family was extremely toxic and abusive prior to me coming out as transgender. The adoption we did was not through legal channels. We had a dinner with a group of friends and signed unofficially adoption papers as a symbol, but we did not go through legal channels due to me getting gender affirming top surgery in December, and my bio mom's insurance is better than my adopted dad's, and my bio family is leaving me on the insurance, which is covering my surgery.

I'm looking to change my last name to match my adopted dad's name. I am no contact with my bio family. I had a legal name change earlier this year for my first name to change to my preferred name, and my bio mom had to go through her employer to get my name changed on the insurance policy. Because I'm no contact, I don't want to contact my bio mom to have my name changed if I do a legal name change. Can I call her employer and have it changed myself without going through my bio mom? I know where she works and I know the person I would need to get in contact with to change my name on the insurance policy. Is this possible, or should I wait two years until I'm off her insurance and have my own?

Any advice or input would be appreciated :)

Edit: I should specify a few things

1. I am not trying to go onto my adoptive dad's insurance. The adoption was symbolic, so that's not something I'm considering or thinking about.
2. I would not change my name until well after my surgery and recovery are over and done with to avoid any potential problems
3. Legal name changes in NJ can change the last name without much problems, especially over 18.
4. I'd like to take whatever route avoids contact with my bio mom
5. I can't currently afford my own insurance as I'm a full time grad student and only work part time