PISCATAWAY, N.J.—The biggest display case in the lobby of the Hale Center, home of the Rutgers football program, has been updated to include the uniform of Khaseem Greene, the hard-hitting, outgoing outside linebacker—plus a giant new trophy.

Last season, Greene helped the Scarlet Knights win their first Big East football title in 20 years of trying. Rutgers had to share the title with three other schools, and then suffered a soul-crushing collapse against Louisville with the Big East's Bowl Championship Series bid on the...