The Secretary of the military department concerned shall issue a certificate of discharge or an order of acceptance of resignation in the true name of any person who was separated from the Army, Navy, Air Force, Marine Corps, or Space Force honorably or under honorable conditions after serving under an assumed name during a war with another nation or people, upon application by, or on behalf of, that person, and upon proof of his identity. However, a certificate or order may not be issued under this section if the name was assumed to conceal a crime or to avoid its consequences.