Op,
This is going to sound harsh, but I suspect you already know...
You were a bit of fun for this man. Nothing more. He never had intentions of leaving his family for you. He used you.
He now has an issue...his indiscretions are about to become public and this risks his family life as he knows it. At this point he wants the problem to disappear...that’s you and your baby.
If you keep the baby, he will resent you. Resent the child. Possibly abandon you both in favour of trying to win back his
If you abort the baby, he will run like the wind and never look back. You will be left to grieve alone. He will not hurt, trust me. It will be a relief for him.
You are both equally responsible for the position you are in. He cheated on his gf, which he clearly regrets now. You chose to sleep with a man who treated another woman like this. He is utterly despicable and you haven’t behaved that much better.
You will never have the option of putting on social media who the dad is and feeling happy and proud about the impending birth in that regards. So, what difference does it make if he asks not to be named? It’s either ‘I don’t want to say who the dad is because we are no longer together’ or ‘the dad is this guy...who already has a gf and child’. Neither sound that appealing to me. But those are the consequences of both of your actions.
So what to do? Well, I don’t think this low life of a ‘man’ should get away with what he has done, so if you want that baby, then you keep that baby and cherish it enough for both of you. Love it. Explain the truth regarding his or her father when the time comes. They will understand there was nothing else you could do. Claim financial support from the CSA; he will have to admit the situation to his gf and deal with those consequences too.
Don’t worry about putting his name on a birth certificate. He’s not going to be in your lives anyway, he’s making that plain for you.
Move on from him and look after you and the baby... and in future, choose a partner who is available and who is not a liar or a cheat and save yourself and any future children the same unnecessary heartache.