that is acceptable. Univesity of Texas is simply called Texas.

Including the mascot is also typical, which would make it Brigham Young Cougars. When I work with FoxSports, they require that the first reference to BYU be "Brigham Young Cougars" that is the what their system uses to categorize BYU related stories.

Some schools have come out and designated the abbreviation to be the offical name, at least as far as sports is concerned. UCF is one. That is the brand they have chosen to be known by. As far as I know, BYU has not taken this position.