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

When I was born my parents were not married and I was given my mother's maiden name.

Around the age of 5 (1986) my family applied for food stamps and one of the stipulations, I guess, around the time was for last names to match in the household. My mother was able to change my last name on my Social Security without any court documentation to my Fathers last name. This was able to be done through the school system.

Before this change happened my mother obtained a few backup SS cards that still had her maiden name.
When I was 16 and when I obtained my ID/DL I used one of these old ID cards. (I was stupid and it was the easier route, as I didn't have any of the correct SS cards)

My SS has my fathers last name
My ID/DL and BC have my mothers last name

This is leading to employment issues because my name doesn't match my social, so my background checks will not clear.

I want to retain the name on my Birth Certificate, and drop my mothers maiden name off my Social due to me and my daughter sharing the same last name (the BC name)

What is the route for me to take to have my Birth Certificate, Social Security and ID to match up again? Ideally changing my SS card to match my BC And ID.