Getting a name change is not a criminal legal matter, you should consult a civil attorney. This website https://www.dshs.state.tx.us/vs/reqproc/faq/amendment.shtm#I%20need%20to%20change%20my%20last%20name%20(or%20my%20child%27s%20last%20name)%20on%20a%20birth%20certificate.%20What%20do%20I%20need%20to%20do?
appears to claim you can do this for $37.
These statements do not constitute legal advice. They are meant to be general in nature, for any specific legal questions you should always seek the counsel of an experienced attorney.
Each lawyer sets his or her own fee for the work. So, you will need to shop around.
Answers on Avvo are for general information purposes only and should not be relied upon as legal advice. No attorney / client relationship is created by providing this answer. For specific advice about your situation, you should consult a competent attorney of your choosing.