An annulment is permitted in the Catholic Church when two people want to end their marriage and still be able to receive the sacraments. Many questions are asked, many papers filled out, and people interviewed to obtain information that leads to information that proves the marriage should never have taken place.
Children born to the couple during the time they were married maintain the father's name unless somewhere along the way, the mother kept her name when she was married, or had the child by a different man and the baby had his name.
Later on if the woman remarries and the new husband wants to adopt the children, and the natural father agrees to it, then the children can get the name of the adoptive father. Until that time they keep their name at birth.
Children born to the couple during the time they were married maintain the father's name unless somewhere along the way, the mother kept her name when she was married, or had the child by a different man and the baby had his name.
Later on if the woman remarries and the new husband wants to adopt the children, and the natural father agrees to it, then the children can get the name of the adoptive father. Until that time they keep their name at birth.