Can the mother still get child support if the last name of the baby is not my last name but hers

Yes.
The child's last name could be "X" and if you're the father you're still financially responsible.

The only way you are going to get out of child support is if you either PROVE that you are not the father (by DNA--and many states, there is a time limit on this) or if there is a step-parent wanting to adopt.

Just pay your child support, please, so that *I*, as a taxpayer, don't have to pay for YOUR kid.