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

Thank you. My son has legal lcustody of his biological daughter and wants to change her last name to his. She was born in Ill. but has lived with her father in Houston since 2001. Her mother lives in Il. and does not contest. What is the easiest and least expensive way to get this done? He is a firefighter and the child's mother contributes nothing to her support. He has been told by the Harris co. clerks office that he needs to have the child custody moved to the state of Texas. Is this necessary? He has the custody papers in his possessions. Is a lawyer necessary?