National Commission on Modernizing Military Installation Designations Act This bill establishes in the executive branch the National Commission on Modernizing Military Installation Designations, an independent commission charged with reviewing the designations (i.e., names) of certain military installations and other property of the Department of Defense (DOD). Specifically, the commission must review the designations of the following military installations: (1) Camp Beauregard, Louisiana; (2) Fort A.P. Hill, Virginia; (3) Fort Benning, Georgia; (4) Fort Bragg, North Carolina; (5) Fort Gordon, Georgia; (6) Fort Hood, Texas; (7) Fort Lee, Virginia; (8) Fort Pickett, Virginia; (9) Fort Polk, Louisiana; (10) Fort Rucker, Alabama; (11) the U.S.S. Chancellorsville ; and (12) any other military base or property as the commission determines appropriate. In conducting its review, the commission must consider whether current designations represent the values enshrined in the U.S. Constitution and whether a designation features certain other characteristics (e.g., honoring careers or actions that were important to, and well known in, the locality or function to be memorialized). The commission must produce reports with any recommendations for action by the executive branch and Congress related to each military installation. Not later than 30 days after the submission of the recommendations in the final report, DOD must redesignate the military installations with such designations as determined by the commission. The commission shall terminate not later than 30 days after submitting the final versions of its reports and recommendations.