What rights regarding access does have a father have when not named on a child's birth certificate?

If he is the father of this child, he should go to court, via a lawyer, and request visitation.

He should also be prepared to pay child support as well of course.

As to the birth certificate, as your attorney about how to go about possibly changing that.

On the birth certificate or not, if he's the father, he has the same rights either way.

HOWEVER--Men must go to court to get their rights instated.

Get a lawyer, go to court, and get child support, custody, and visitation worked out through the courts.