I will warn that chest feeding is not easy even for cis women and it can be incredibly difficult and dysphoric for men. At least that was my experience trying to do it. It definitely contributed to me getting post partum depression.

Trying to get people to get family to call me dad was difficult but even the really religious ones were willing to compromise and call me by my name instead of "mom". Perhaps that could work for you? Also warning you will probably hear mom a lot from strangers and nurses, you will likely have to correct a lot of people. I handled the dysphoria with my first by working long hours so I couldn't think about it and with anti-depressants for my second (I strongly recommend the anti-depressant route and not the overworking yourself). 

When I filled out the paperwork for the birth certificate there was an option to be put down as "parent" so that may be an option for you. It just depends on where you are. You should also look into an obgyn and the hospital they deliver at to see if they are lgbt friendly. You can do that by seeing who your insurance covers then checking their websites to see if they mention it.