New York State has one College & University system, and every school officially named "The State University of New York at...". Probably because NYU, it isn't UNY, it's SUNY. Awkward. It's been that way since at least the 1960s. So the official name is "State University of New York at Buffalo". They finally came up with "University at Buffalo" to shorten it. It works, I guess. For other than sports, you'll probably see SUNY Buffalo.
Stony Brook is another SUNY university. There are two others, Albany and Binghamton, and I don't know what NCAA level those are, but they aren't Div I. I'll never understand why they decided to have 4 equal universities, and not make one (Albany?) the flagship school. Too late to ask Nelson Rockefeller, or Robert Moses.
Worse yet, naming-wise, are all the smaller colleges in the system, whose names are officially "State University of New York College at...", such as "State University of New York College at Fredonia" (yes, there is such a place, just outside of Buffalo).