My question involves adoption law for the State of: Texas

I was pregnant at the time that I was adopted as an adult. When we filled out the birth certificate information for our child, I gave them my adopted last name as my maiden name because I thought, being adopted, that my maiden name would now be my new father's name.

A year later, I just ordered a copy both of our birth certificates. My name on my birth certificate is still listed as my biological father's last name, even though my adopted father is listed as my father. Is this normal?

If that is correct, how do I go about correcting my maiden name on my child's birth certificate? All of the forms I see involve changing the father's name.

Thank you, in advance, for any information!