If my girlfriend's Ex-husbands name is on our sons Birth Certificate, can she still have me pay child support?

It's a real scandalous situation, and the 2nd part of my question would be, how is his name on the B. Certificate? She says the hospital did it on their own because they were married and thats where they had their daughter (same hospital). But, didn't she have to fill out a form or something stating she was the mother & who the father is? She would have to be the one who put his name on it... Right?