First of all, welcome.
Here are my thoughts. You can name a kid whatever you want, whether it's your name, his name, a combo of both, or something completely different. There is no law that I know of which requires the kid must have the same name as the parents, or that it must be legal parents, so don't fret about that. Tradition and convention are not the same as legal.
Also, there are plenty of unmarried mothers having babies with friends who assist them, or family members, instead of spouses. He is part of your family; that's all the hospital staff would need to know. As long as you give permission for a particular person to be there with you, your wishes should be honored. The doctor or midwife and hospital staff are adults and if they have judgments about a patient's living situation, so what? They should still behave as professionals and keep it to themselves, even if M. is all cuddly and lovey toward you and then subsequently his wife another time. Why not have the wife there, too?
You can have a type of non-legal ceremony to acknowledge your relationship and make vows. It won't be recognized by the state, but as long as the ceremony is meaningful to you three, that could be very satisfying, I imagine.
As far as public displays of affection, it sounds to me like that is something you have to work out among yourselves, make some kind of agreement of how to handle awkward moments, or how to "come out" to people. No, you're technically not a second wife, but there are people here who have shared their experiences of being public as the girlfriend or whatever. Why not read through the "Life Stories and Blogs" section? Unfortunately poly people still have to deal with lots of puritanical thinking and judgment directed their way, and so you have to figure out what level of "out" feels comfortable and safe for you. Maybe there are other poly people in the community you can befriend, with whom you will feel safe and able to relax and be yourselves.