Original sentence: In Commonwealth Realms (which share the same monarch as the UK) passports are issued in the name of the governor-general of that state on behalf of the Queen, except in Canada, where passports are issued on behalf of the Queen by the Minister of Foreign Affairs.The British monarch does not have a passport as British passports are issued in the monarch's name
Edited sentence: Though Elizabeth II is separately monarch of sixteen countries, she does not possess any passport as in each state passports are issued in her name as Queen of that particular kingdom, either directly, as in the United Kingdom, or in the name of the governor-general of that state on behalf of the Queen, except in Canada, where passports are issued on behalf of the Queen by the Minister of Foreign Affairs