Well he's done you a favour. As others have said, you need to turn around your thinking on the birth certificate. It isn't so much about him giving you/your child the 'gift' of his acknowledgement... it's MUCH more about YOU giving him parental rights that, quite frankly, could turn out to make your life much, much more difficult if your relationship breaks down.
If I were not married to the father of my child, no way would I automatically put them on the birth certificate. And no way would I ever consent to my child not sharing my surname - the very idea of that when I were definitely gonig to be main and only carer - LOL. I'm glad to see you're definite on that one!
Don't engage with him now at all. Register the baby quietly with the names you want, and if he changes his mind and wants to be there, say no. Or even change the date and don't tell him if easier - just make damn sure he's not on that BC. You're lucky this happened!
Needless to say, also don't tell him that him being on the BC makes no difference to CSA/maintenance. You say he's self-employed, it's probably likely you'll get little anyway. Register your baby, then make a claim. For those saying he should have the option to opt out - um, no. Men get the option to make sure they aren't fathering babies they don't want to support financially at the point where they choose to wear a condom or not. Simple as.
But - maintenance and contact are separate things. It's undoubtedly in your child's interest to have a committed relationship with their dad. But.. ONLY if he's committed. So while I don't agree with the knee-jerk 'If he isn't going to pay maintenance he isn't seeing him' - I think that really you're probably saying something quite different and something more understandable... ie, if he's going to see himself as 'not committed' and intends to drop in and out when he fancies playing daddy every now and again - then no, a flat no. That definitely is NOT in your son's best interests.
But make sure you separate the two. Start the claim, let that run on its own. Refuse to discuss it with him.
Then, contact. What does he envisage? What is his idea of a relationship? If it's a vague 'Oh I'll try and come down every few weeks' - then you're well within your rights to say - sorry, no. You're not going to play Weird Uncle who comes with presents. And you are not going to dictate the terms either - there will be no 'Keep the weekends free this month because I might feel like coming down.. .oh sorry, can't now, something's popped up.' You are either a dad to him, or you are not. Contact doesn't have to be every week, but it has to be - consistent, committed, and FATHERLY - with a view to him taking responsibility at an appropriate pace, which will ultimately end in your DS staying over when he is older, regularly.
If he balks at that and wants it free and easy - nope. See you in Court if you want to argue that you should be allowed to see him when you fancy and let him down at will. If he's responsive and willing to talk it through - then talk.