Does a father have automatic rights if baby is given his last name?

I am married with three children & separated, though not legally. Babys father is married with two children & separated, also not legally. I would like to avoid having the state enforce the "legal spouse automatically responsible" issue but also want the babys father to seek his rights by his own merit & efforts. What is the best way to go about this? Id love to give the baby his last name but I know we will never be together and don't want to hand over equal rights. He's shown very little interest and plans on trying to back to his wife where she plans on playing house as often as possible. They also live out of the county an hour & 1/2 away. All things considered, I think he should have to make the effort to gain rights. Thank you very much!!