Im married to someone but we have been separated from each for months, I just found out that I’m pregnant with my current partner baby. When I give birth would they let me put my baby father on the birth certificate or would they just think the baby belongs to my ex husband?

My ex husband has told me he has file for divorce but he all of a sudden stop communicating with me and left his job and moved I have no idea how to find him even just to make sure his okay…

I just don’t want him to be responsible for a child that isn’t his.