Proving my baby is his

I’m 16 weeks pregnant. The father of my child does not believe this baby is his. He basically isn’t in our lifes hasn’t been for a month now. I’ve told him many times it is his and that I want to have a family but he doesn’t seem to believe or want that. I’m gonna go thru w the pregnancy of course. As soon as my baby is born I’m getting a DNA test. I will tell the father to come to the hospital just to get his DNA but I won’t allow him to see the baby. It’s going to feel amazing to give him the results so he can hurt as much as I am going thru my pregnancy alone. After that he will have to work hard to see his baby after denying him. I know for a fact he will want to be a part of the baby’s life once he knows it’s his. Any advice on how I can go thru w this? On how things should be after the baby is born and proven to be his? Any of your ladies went thru the same thing ? I don’t want my baby to have his last name because of this whole situation. What should I do ?