well, here's to answer the ?. even if he's on the birth certificate, if you were never married, he has no rights to custody of your son.
the bio father would have to sign off since he is listed on the birth certificate.
you would not have to change your child's last name to the adoptive fathers that would be his choice.
if you die, and husband is adoptive father, than no the bio father has no rights.
if husband adopts the bio fathers child support is completely stripped. he is no longer anything to your son, so he has no responsibilities.
if this is something that the 3 of you really want, and the bio father is nowhere around and doesn't want visitation, etc. you could try to open an adoption case with an attorney...however, once the court is involved, visitation, etc might come up. so think carefully.
and to respond to Jennifer S. terminating parental rights used to not mean that support was terminated also. it had to be specifically noted in the termination papers or support would be ongoing for the child. however, in 03 or 04 (i worked in family law and dealt with this) the orders changed and now when parental rights are terminated child support is also terminated. that doesn't mean that the state doesn't want there money back if you have been getting gov't help.