Does my husband's name have to go onto the birth certificate when my child is born, if I know he isn't the father?

I am currently married, however I am pregnant with another mans baby. My husband was abusive and I was told that I needed to wait until after the baby was born to get a divorce. I don't understand why my husbands name has to go on a legal document claiming a child that is not his. I also don't want to have to ask him to sign the birth certificate, I don't know where he is and he doesn't know where I am and I would prefer to keep it that way.