The mother isn't required to give her child the fathers last name even if they are married. The child should take the mothers last name if the mother is the one who will be doing all of the primary care, ie: Dr.s appointments and school enrollment, etc.
And, he doesn't have to be present at the delivery to be on the birth cert. This is false. Women who give birth when their husbands are deployed still put them on the birth cert. If you are not married the father will have to sign a declaration of paternity and can then be named on the cert. They DO NOT have to be present. That is absurd. What if he doesn't want to see it? They can't force him.