They SHOULD BE, but we are saddled with a city tag as our official name.
However, we are not the only university that has a sports and academic name. Check out these university (not athletic) websites.
Texas - Texas at Austin, UT Austin
Nebraska - Nebraska Lincoln
Wisconsin - Wisconsin Madison
Minnesota - Minnesota Twin Cities
Nevada - Nevada Reno
The examples are endless.
If what you are saying is if we can come up with a nickname athletically that is legal, why can't we also have a nickname academically, be that Louisiana or University of Louisiana?
Fresno State uses that name academically and athletically as a single reference. Yet, it's official name is California State at Fresno.
Virginia Tech also uses that name academically and athletically as a single reference. Yet, it's official name is Virginia Polytechnic Institute and State College.
What is the common denominator? Neither school uses University in their branded nickname. Why can't The University of Louisiana at Lafayette simply use LOUISIANA both academically and athletically? That would certainly help to avoid all of this confusion over our name.