How do I change my son's name when dad's not in the picture?

My son has his dad's first and last name and I want to change it. We're from Texas, but my son and I live in Missouri now, his dad lives in Texas. His dad and I were never married, his name IS on the birth certificate, but he does not pay child support and there has never been a child support order against him. I wondering what my options are and how to go about this. His dad would possibly be willing to sign off on him changing his name.