Baby’s last name on birth certificate

So I was wondering when the baby is born can I pick out a last name for her? So I want to use the Father’s last name but not put him on the birth certificate, will they let me do that or will they require me to put him on there? This is my first child I was just wondering what my options are. Our relationship has not been the best and we are not married I just want to have my options open in case things don’t go well down the road.