Do universities have non greek fraternities?

No, universities don't have organizations officially called "non-Greek fraternities." The term "fraternity" itself refers to a member of a Greek-letter organization. There are many other types of student organizations on college campuses, including social clubs, honor societies, religious groups, professional organizations, special interest clubs, and volunteer groups. These serve similar social, academic, and professional purposes as fraternities and sororities, but they are not considered "fraternities" in the traditional sense.