You're not married, so you're at a disadvantage. If you sign an acknowledgment of paternity at the hospital, you can negotiate over the child's name in association with executing that document. But if your girlfriend does not agree with you, she can simply decline to execute the AOP and give the child whatever last name she chooses.
When you establish paternity you can seek a name change, but when parents don't agree the resolution is often to hyphenate, so that effort may not accomplish much.
Meanwhile, if tis is important to your girlfriend, you effort could damage your relationship with her.
Your precise rights will depend on the laws of your state.

