that depends wrote: Could you name the 15 Commonwealth Nations under the Queen to which you refer?
Google is your friend, as is wikipedia.
Elizabeth II (Elizabeth Alexandra Mary, born 21 April 1926[note 1]) is the constitutional monarch of 16 sovereign states known as the Commonwealth realms: the United Kingdom, Canada, Australia, New Zealand, Jamaica, Barbados, the Bahamas, Grenada, Papua New Guinea, the Solomon Islands, Tuvalu, Saint Lucia, Saint Vincent and the Grenadines, Belize, Antigua and Barbuda, and Saint Kitts and Nevis. As Head of the Commonwealth, she is the figurehead of the 54-member Commonwealth of Nations; as the British monarch, she is the Supreme Governor of the Church of England.
Of course she is actually Elizabeth I in all those 15 other countries (that united under the Scottish crown!) plus Scotland.