My question involves name change laws in the State of: Ohio

My girlfriend wants to change her daughter's last name to hers. Her ex is currently in prison. The reason he is in prison is because he is the one who caused the severe brain damage to my girlfriend's daughter. His sentence is about halfway over now, and with the daughter being only 2 and a half, her sentence still has quite some time.

My question is: Is there a way to get the daughter's last name changed for free, since she was the victim of a crime caused by her father? If not free, is there a cheaper fee for the circumstances?