Yes, the father has rights and can ascert them at anytime.

And frankly, your CHILD has the right to a complete legal birth certificate. You should put the father on the birth certificate because it's the right thing to do, not because it's convenient for you to forget you slept with the man.

When these questions come up, I often wonder "who's interest is this serving?". It would seem like it is in the best interest of a child to know who their father is and have an opportunity to know his family. It also makes it possible to collect child support, and for you child to be a legal heir should dad pass away with no will. But, most of all, you are giving you child a choice. They can choose, later in life, to acknowledge their father and try to have a relationship, or they can choose to ignore him. You are stealing this choice from your child.

It also makes it easier for the child, when grown, to get medical information if needed.