I have a 2 year old the father left when he found out I was pregnant he's never been around and he's not on the birth certificate he had only seen the baby twice but was doing good about paying child support through child support enforcement of Georgia but now is only pay here and there I'm married now and my son sees my husband as his daddy BC he's always been there I want my son to have my new married last name instead of my maiden name what do we need to do?

Have you considered step-parent adoption? Either that or a simple name change with the court would require notice to the biological father, so might as well go for adoption.

Have you considered step-parent adoption? Either that or a simple name change with the court would require notice to the biological father, so might as well go for adoption. how do I do that and would the father still have to pay child support

Will the father still have to pay child support? And how do I go about the adoption thing?

If the child is adopted, no the birth father no longer pays child support.

In Georgia, anytime the father pays support, that is considered a "contact" even if he does not actually see the child.

In fact Ga will not take away the fathers rights even if he never pays support or never visits.
They may give full custody to mother but will not take away his right to file in court for other latter.

So in GA to merely do a name change, you get the bio fathers permission, and file a name change at the Probate Court office.

The adoption by a step parent also requires a reason ( I see none in your case) or the bio father has to agree. This is often easier, since the bio father gets to stop paying, and is often more willing to sign to save the money

What paper would I get the bio father to sign?