I live in Ohio. I have 2 children with my drug addict abusive ex after leaving him I filed for a protection order of 5 years and it was granted to me. I filed for child support but he never showed to court. I don't want child support just want to know if I can file for a name change or abandonment how would I do this? #please help#

You can't file abandonment, you can file full custody just for your protection. As far as the name change I do believe you have to start by filling out a form at the birth certificate office that has your kids birth certificates.
*of course the father on the birth certificate has to agree and you go from there

You will have to ask him to sign to allow it, if not, you will go to court and show it is in the best interest of the child.

... As far as the name change I do believe you have to start by filling out a form at the birth certificate office that has your kids birth certificates.
...

No, you would first file with the court. If the name change is approved, then the order approving the change is submitted to the vital statistics office.