You can probably "change her name", at least as it is commonly used, simply by having her use your husband's surname.
In terms of changing the birth certificate, that would require step-parent adoption, which in turn would require lawful notification to the biological parent.
Getting a court-ordered name-change without adoption would likely have to be through the court which decided your original custody and support issues, if that has not been changed to another state. You can petition for Texas to assume jurisdiction under the UCCJEA (Uniform Child Custody Jurisdiction Enforcement Act), although it helps to have the assistance of an attorney in preparing and submitting such a petition. The biological father would have the right to be notified of any such court proceedings.

