1. When the father attends registration and is named on the certificate, then the birth is reorded in both names, the child is entitled to use either name.
2. If no father is named on the on the certificate, even if the subsequent husband is the father, the fact that he was not attendant at the time and was not named, would mean the child would have to be adopted by both parents as a couple, regardless of the fact the woman is already the child's mother.
From a conversation with a Registrar some time ago, when discussing the different events that can arise, I believe my answer to question two is correct. I am sure Stan will soon correct me if I am wrong.
Jebber