I recently went up to Fresno State on a recruiting trip for my job. I had never heard the University called anything but Fresno State. When I arrived on campus, I noticed that the proper name of the school, which is "California State University Fresno" was everywhere; on signage, stationary, brochures, etc.
Even though the proper name of the university was used in many cases, they do not seem to have any problem with branding themselves as Fresno State. (Their official website does say Fresno State)
Just an observation