There is no age restriction for name changes. A parent can petition for a name change on behalf of a minor. However, the child's legal father will have to be served notice of the request for the name change. Also, the child's name may be changed only if the name change is in the child's best interests.
Once a person turns 18, the person can do the name change without either parent's permission. However, I had a judge refuse the change one person's name because the lady had a criminal juvenile record.
The other attorney that answered this question is absolutely correct. The bio. dad must be notified. He can object to the name change. Then it will be up to the judge to decide if it is in the children's best interest to have a name change. I don't practice in San Antonio so I don't know what the judge will do.
I assume that you will be retaining the services of an experienced family law attorney in San Antonio that practices in the San Antonio family courts on a regular basis and I would rely on their experience and expertise. If they tell you that it's a waste of time, then I would tell you not to waste your money moving forward with the name change.