In order to receive child support does the child have to have the father's last name?

Nope. As long as he's proven to be the father, he pays child support, regardless of names.

No. As long as he's the father, it doesn't matter what the baby's name is, he has to pay.

No, in many cases the mother may not even know for sure who the father is and will have to have two or three men tested to find out.

Then she can sue that one for support.

All they have to prove to the court is who the father is.

No the child does not have to have the fathers last name. As long as he is the boilogical father and there has been a DNA test to prove it then he is obligated to pay child support