When the mother of a child is unmarried at birth in Illinois, the father’s name cannot be added to the birth certificate until paternity is established. This is the case even when the parents are engaged or cohabitating at the time of the birth. In a situation in which a mother is separated but remains married and has a child with someone outside the marriage, the individual the mother is married to is legally presumed to be the parent of the child.
Unpaid child support obligations aren't something that parents in Illinois should ignore. The penalties for being a "deadbeat" parent are severe.