National Commission on Renaming the J. Edgar Hoover FBI Headquarters Building Act of 2021 This bill establishes the National Commission on Renaming the J. Edgar Hoover FBI Headquarters Building. The commission must make recommendations for redesignating the building that reflect certain considerations, including the mission of the FBI, the values of the U.S. Constitution, and racial, ethnic, and gender diversity. The Director of the FBI must determine whether to redesignate the building in accordance with the commission's recommendations; if the Director declines to do so, the Director must submit an explanatory report to Congress.