Legal Question in Family Law in Texas

You probably need to talk to an experienced family law attorney.

Has the "father" been legally declared to be the father?

The parents can agree to whatever they want to do.

If the father wants the child to have his last name, the judges in Harris County will order that the child's last name be changed. However, if the parents agree that the child retain whatever last name the child currently has, the judge will not force the child's name to be changed.

I hope this answer is helpful. It can get very confusing. That is why I suggested that you talk to an attorney.