Why use article 'the' in the phrase The university of Texas at Dallas?
The founders of UTD named it "The University of Texas at Dallas" while the founders of UF named it "University of Florida". What was the reason the article "the" was used?
In your name example
"The" is used because it is the official name of UTD.
In your specific case, why the Texas University System chose to use "The" is anyone guess, maybe because they are Texans loud and proud. One notes that in the more laid back land of the west coast, the University of California System decided not to use "the"
And also their campus are named "UC something".