This is a red flag that you need to deal with now. You can either go into denial about this and have it possibly come back to bite you later or you deal with this head on the way it should be.When I told her bio dad that I was getting married, he said that he wouldn't allow her to have my husband's name and that he is her father...
Consult with an attorney. Get the legal ball rolling to establish who the father is and ensure he is ordered to pay support and establish each others rights and responsibilities in this matter. If he really does not want to be involved, he may reconsider his position on allowing adoption when faced with the prospect of 18 years of child support payments.

