I think that's because its full name is "State University of New York at Buffalo". So the "of" is already taken in the complete version.
Or it could be that way in order to differentiate it from that other former State University of New York Buffalo, which is now known as Buffalo State College.
Is State University of New York at Buffalo, or University at Buffalo for short a flagship of SUNY system?
There used to be two SUNY Buffalo schools. Now they are University at Buffalo and Buffalo State College.
Not sure if University at Buffalo is the flagship, but there are four SUNYs that offer doctoral programs: SUNY Albany, SUNY Binghamton, SUNY Buffalo, and SUNY Stony Brook.