The simple answer might be that a state often has more than one large university and they both need names, so there are different formats.
However, this doesn’t explain why the second university wouldn’t just pick a different name entirely. Indeed, most states have more than two universities in their system, and the third one always has to pick a name not of one of the two common formats.
Some of it has to do with two laws in the late 1800s which gave land to the states to create universities – the Morrill Acts. These laws gave federally-owned land (which was mostly taken from indigenous tribes) to establish colleges for the teaching of agriculture and trades. The resulting institutions are known as “land grant universities.”
Here is their intended purpose, from the U.S. Code:
[…] to teach such branches of learning as are related to agriculture and the mechanic arts, in such manner as the legislatures of the States may respectively prescribe, in order to promote the liberal and practical education of the industrial classes in the several pursuits and professions in life.
Since, by the time, there was often already a “University of State Name,” these second “flagship” universities were often named “State Name University.” This “second” state university is usually (with several exceptions) smaller than the University of State Name, less prestigious, and – as the law dictated – tends toward agriculture, engineering, and other trades.
This still doesn’t totally explain why the land grant school didn’t just pick another name entirely, but it does explain why many states created a second large university – they were given land to do this, and presumably, most wanted to accept it.
Here is a map of all the land grant universities. They seem about evenly divided between (1) University of State Name, (3) State Name University, and (3) something else entirely.