I want to change my son's last name to mine... I am his legal mother and I am the only parent on the birth certificate... Do I still need the father to sign any paper work in order for me to change his last name?

This is a depends on where you live, in the US it will be a state by state issue. Some of the stickies on family law on the may be of some help.

Easiest way, go to the court in your state ( in in the US) that does the changes and just ask them. It is a simple fill in the blank form normally and does not cost much. There are online sites offering to do the paper work if needed.