My response:
Certainly, you can give the baby your name. However, in the long run, it will cost you more should you later decide that you need child support. If you place the father's name on the birth certificate, and he signs a Declaration of Paternity, you won't have to spend time, money and grief later on in order to obtain child support.
If he refuses to sign a Declaration of Paternity, then you can still place his name on the Certificate; but, you'll have to go through the process of proving paternity.
IAAL