My girlfriend is pregnant and the biological father wants nothing to do with the baby, I want to know if I can put my name on the birth certificate?

No you may not as you are not biologically related to this child.

NO, if your state allows for adoption of a child by a lesbian couple ( will assume you are a couple by the question, since you are wanting to take the fathers role)

But if your state allows for same sex couples to adopt, then you can file to adopt the baby and allow the bio father to sign over his rights.