Use Michael A. Middleton Center for Race, Citizenship, and Justice on first reference (note the comma before the and). Middleton Center is acceptable on second reference.

A partnership between the School of Law and the College of Arts and Science, the Michael A. Middleton Center for Race, Citizenship, and Justice promotes excellence in the multidisciplinary study of race, citizenship and justice in the United States.

Example: The Michael A. Middleton Center for Race, Citizenship, and Justice is a partnership between the College of Arts and Science and the School of Law.