Changing a Child's Name, No Legal Father Established

My question involves name change laws in the State of: Texas

Sorry if this has been asked-

My daughter was born in California and we now reside in Texas. There is no father listed on the California birth certificate so what would I need to do to change her last name? I'm changing her last name to mine because he has not been there since birth and has finally said he wants to sign over any parental rights (if any)

Another question is : if he is willing to sign over any parental rights, what do I need to do since he was never listed on the birth certificate?

I know Texas law requires both parents or terminated by law parent to have documentation on the Petition for Name Change.

Thank you!

If you are married and your new spouse wants to adopt, you can have him consent to stepparent adoption. If the father's parental rights have been established and you want to terminate the father's rights rights "just because", you can file a motion with a Texas court and attempt to convince the court to do so. See Texas Family Code, Sec. 161.001 et seq. If the father's parental rights have not been established, there's presently nothing to terminate.

If the father consents to a name change, you may petition the court for the name change and document that consent to the court. If not, you can move for the name change, give notice to the father, and attempt to establish to the court that the name change is in the child's best interest. If dad has not yet established parental rights, I expect that the court would take that into consideration, and would potentially decline to entertain evidence or argument from dad on that basis.

If you care to share the relevant facts, it would be helpful.