Birth certificate

I'm due with my son December 22 and I have a name picked out and the father told me I can use my last name for the baby. The father and I are not together and will not get back together but we are civil and are on good terms for the baby. He wants to be on the birth certificate obviously but I have been told if he's listed as the father the child automatically gets his last name. Is this true? I live in Florida if that changes anything.