Linde,
I just Googled "How to change name and gender on US naturalization document" and had multiple hits. Some are transgender help sites. One of those listed the form number, which I clicked. The non-refundable charge is $410.00 for the application fee plus $85.00 if they require biometrics. I think that means finger prints and maybe eyeball scans. I would recommend checking all these help sites plus the US Government site for helpful hints and instructions how to fill out all the forms. That is what I basically did to change all my documents, research, read, ask questions, fill out and submit. with all this immigration issues right now, there are many, many respectable immigration lawyers out there, and some may include pro bono help to fill out forms correctly. Good luck.
I still need to change my car registration, but need a copy of car title too. Since I will make my last payment this week, I will get my title from my lender after that with no lien on it. The other last major thing is my birth certificate in Michigan (I live in California). They require a notarized letter from the doctor who does a gender reassignment surgery (their words). I read that an orchiectomy should be good enough, but I am going to wait for my BA and have that doctor fill out, sign and notarize that form.
Good luck and I agree, you may sleep better knowing that you have that corrected document in your own files all officialized.
Allie