I just had a baby not to long ago and gave him my last name now the baby's father is wanting me to give him his last name. Should I and how would I ? Make it known that me and the father are not together.

I'm not sure the exact situation you are in abd may not help telling you yes or no but just an fyi based on research that I have done it is easiest to do it before the child is 12 months old after that you need to go to court.

Well, the father is not interested in the child except to get his last name? Personally I would tell him to go pound sand. The name stands unless he wanted to marry me and raise our child together.

If the father doesn't want to have anything to do with the child then NO do not change the child's last name.

Why do this?

I married my wife, who had a daughter with a man years before. The man had no part in the child's upbringing. She gave her daughter her last name. When we married, my wife added my name behind hers, and the daughter kept her mothers name with no change.

Why change the name? What is the purpose? To get him interested maybe in time? To give the child a connection to a father, even if he isn't present?

Personally, I just don't see why to change the name... not at all. But you have some reason to consider this... what is your thinking?