If I am not divorced from my husband, can I put the real father's last name on the birth certificate?

In Massachusetts, if you are married at the time of the birth of the baby, the baby is considered to be born of the marriage and the legal child of the other spouse.  You must file a complaint in equity within 60 days of the birth of the child in the probate and family courtto address the actual paternity of the child, or the real father will lose all his rights to the child.  Time can be very sensitive in this situation.  I would strongly recommend contacting an attorney immediately upon the birth of the baby to address this issue.