I see this as two questions: 1) should adopted children have the right to know the identities of their biological parents; and 2) should adopted children have a right to a relationship with their biological parents.
So, yes, adopted children should have the right to factual information about their own births, including whatever names are listed on the birth record. Typically, the name or names of parents will be on the original birth certificate (OBC), the one that is created when the child is born and the one that remains unchanged even after an adoption. Unfortunately, most states do not allow access to the OBC, even to adult adoptees. But it should be a right to know that factual information once the adoptee becomes an adult.
But, no, adopted children don’t have a right to a relationship with their birth parents once that relationship is terminated through adoption. You cannot force a relationship with anyone, and it would be pretty nuts to try to do so.
Access to the original birth certificate is a right; reunion is not. Many adoptees and others overlook this important difference.