I don’t think surname matters much but I’m really sad to see all the posters on here encouraging OP not to put this young man on the birth certificate.
For one thing, a birth certificate is a statement of fact. The fact here is known - this young man is the baby’s father.
More importantly, children (in the absence of violence or drug use which is not mentioned here) need fathers! It doesn’t matter that the OP no longer wants a relationship with the father. That’s her right, but the child also has a right to a relationship with the father, & with the extended family. The more hostile the OP is to him, the more obstructive and exclusionary, the more difficult this will be - and not putting him on the birth certificate will be a hostile act.
There is as far as I can see from what has been said in the OP no reason at all why he should not be on the birth certificate.
In this case I think this is made even more pressing by the fact that in all honesty the OP has been irresponsible. Having a child with someone you barely know, who you haven’t even been on a date with, is a dreadful idea. I think the more adults that are involved in this child’s life, the better, because they may be particularly needed in this case. So that means extended family & father too.
I have 3 children, one of whom has a life changing disability. This has really brought home to me the immense responsibility in having a child - how difficult it is, how much may go wrong, and how wrong it is to have a child without thinking through that this is not just a baby - it is a person, who may have complex and unforeseeable needs that will change over time, and who will benefit from a strong relationship with both parents. Sometimes I get the impression that posters here see children as ‘my baby’, almost as pets, as little babies frozen in time who will just need milk. This is not the case.