In general, the use of “University” or “College” can be dropped in most sports contexts. Every effort should be made when writing to make it obvious to the reader that the college is being referred to, without the usage of those words.

Examples:

Arizona defeated Wisconsin on a last-second touchdown pass.

Andrew Benintendi, an Arkansas alum, won a World Series with the Boston Red Sox in 2018.

Some institutions follow unique naming formats, even in sports contexts.

Boston College
Boston University
Buffalo
BYU
Cal Poly
Cal State Fullerton (Bakersfield, Northridge, etc.)
Fresno State
Long Beach State
LSU
Miami (Ohio)
MIT
NYU
Ole Miss
Penn
Penn State
Sacramento State
San Diego State
San Jose State
SMU
SUNY Oswego (Farmingdale, Brockport, etc.)
TCU
UAB
UC Santa Cruz (Irvine, Riverside, etc.)
UCLA
UConn
UCF
UMass
UNLV
UTEP
USC
UT Arlington (Dallas, etc.)
VCU