
YMMV depending on insurance, but coverage was a complete non-issue for me (full hysto/oopho). First, check your coverage for transition-related procedures. You should be able to find what specific surgeries are covered and what the requirements for coverage are. Then, find surgeons in your area who accept your insurance and check their requirements as well. My insurance provider was able to give me a list of them over the phone that had worked with trans men.
I got this procedure (hysto) covered under my insurance. I was able to get my ovaries and cervix removed too. I'm extremely privileged to have not had to pay for anything, but YMMV depending on location and insurance. Paradoxically, I feel like it was easier for me to get a hysto as a 21 year old trans man (because it's covered under the gender dysphoria diagnosis) vs a cis woman around my age because she'd get a lot of pushback.
You’ll likely have to obtain a referral letter from a psychologist, so either work on that next or while you’re looking into the other things (just make sure it satisfies both the insurance and individual surgeon’s requirements). After that, assuming you meet all the other requirements, just give a surgeon a call and book a consultation.