Naming the University

The preferred usage is the full name:
The University of Tennessee at Chattanooga
or its initials: UTC

Avoid the use of hyphenated forms:
The University of Tennessee-Chattanooga


The University of Tennessee, Knoxville; or UTK
The University of Tennessee at Martin, or UT Martin (no hyphen)
The University of Tennessee, Memphis; or UT Memphis (no hyphen)
The University of Tennessee Space Institute, or UTSI

All the campuses together are the University of Tennessee. (Note the lowercased the. Although the is part of the legal name, system policy lowercases it in all but the most formal situations.)

Also, lowercase system in UT system.