Changing a Child's Name: Changing My Child's Hyphenated Last Name

My question involves name change laws in the State of: Texas
My son's legal last name is hyphenated with the mother's last name first and my last name second. The mother passed away last year.
I am sole conservator of my son per court order. I presume I have to go through the legal system to change the last name to just
be my (the father's) last name?

Changing a Child's Name: Changing My Child's Hyphenated Last Name