Sounds like a buncha' shit to me. We've officially been "The" University of Texas since the adoption of the current Texas Constitution in 1876, wherein Section 10 of Article 7 reads:
"Sec. 10. ESTABLISHMENT OF UNIVERSITY OF TEXAS; AGRICULTURAL AND MECHANICAL DEPARTMENT. The Legislature shall as soon as practicable establish, organize and provide for the maintenance, support and direction of a University of the first class, to be located by a vote of the people of this State, and styled, "The University of Texas", for the promotion of literature, and the arts and sciences, including an Agricultural, and Mechanical department." (bolding added; quotation marks are a part of the Constitution)
And in case anyone was wondering, the constitutional mandate that The University of Texas be a "university of the first class" is what differentiates us from the fuckin' aggys. And the fuckin' sooners. And the fuckin' bucknuts. And the fuckin' . . .