score:12
If past practice is followed, she would be Queen Mary III. However, ultimately, it will be up to the monarch, on the advice of the Accession Council to make that decision.
The current rule was described by the then Prime Minister, Winston Churchill, in a Parliamentary answer on 15 April 1953:
Since the Act of Union the principle to which my right hon. and gallant Friend refers has in fact been followed. Although I am sure neither The Queen nor her advisers could seek to bind their successors in such a matter, I think it would be reasonable and logical to continue to adopt in future whichever numeral in the English or Scottish line were higher. Thus if, for instance, a King Robert or a King James came to the throne he might well be designated by the numeral appropriate to the Scottish succession, thereby emphasising that our Royal Family traces its descent through the English Royal line from William the Conqueror and beyond, and through the Scottish Royal line from Robert the Bruce and Malcolm Canmore and still further back.
(my emphasis)
Mary II ascended to the thrones of England, Scotland, and Ireland in 1689, as joint sovereign with her husband, William III. That is the highest regnal number for a Queen Mary in either England or Scotland, and so the next Queen Mary should be Queen Mary III, if the practice set out is followed.
Note that Churchill (and the Queen) was careful not to seek to bind future monarchs in this matter.
However, you are mistaken on one point. Specifically, when you say that:
This means that the current Queen is "Queen Elizabeth II" for all of the UK because she is the 2nd Queen Elizabeth for the united crown, even though Scotland never had a 1st.
Queen Elizabeth II isn't the 2nd Queen Elizabeth for the United Crown (Elizabeth I was queen of England only, and only Queens Regnant are counted).
As is made clear in the Parliamentary exchange linked above, she is Queen Elizabeth II because there had been one Queen Elizabeth in the English line and none in the Scottish line, therefore the English line gave the higher number.
EDIT (requested by Spencer in the comments below)
When it comes to regnal numbering, only kings and queens regnant are counted. So, should we one day have a King Albert in the UK, he will be King Albert I, since Queen Victoria's husband, Albert, was Prince Consort, and not King.
This is relevant to this question becuase, George V's wife, Queen Mary was Queen Consort, and not Queen Regent. She was therefore not Queen Mary III. This contrasts with Mary II who, as mentioned above, ruled jointly with her husband, William III, and was thus Queen Regnant, and not Queen Consort.
Upvote:3
As sempalscuba said in his answer, there is no way to be certain what numeral a future monarch will choose to use, but going by the practices in the past it is most likely that a future queen regnant of the UK named Mary will known as Mary the Third.
I note that if Prince George (born 2013) has children, as he probably will, and if his oldest child is a girl and is named Mary, that will be the soonest that another Queen Mary could reign in the UK. And considering the average length of generations in the Royal family and the present age of the Queen, the hypothetical oldest child of Prince George, whatever his or her first name will be, will probably not reign until about 2100.
However, I can point out that it would be equally logical for the next queen regnant of the UK to be known as Mary the First.
The Kingdom of Scotland dates aback to AD 843, more or less, and the Kingdom of England to 927. In 1542 King Henry VIII of England turned his Lordship of Ireland (created in 1177) into the Kingdom of Ireland. In 1707 the Kingdoms of England and Scotland merged into the new Kingdom of Great Britain. In 1801 the Kingdoms of Ireland and Great Britain merged to form the United Kingdom of Great Britain and Ireland. In the 20th century most of Ireland broke away from the United Kingdom and the title of the Kingdom was eventually changed to the United Kingdom of Great Britain and Northern Ireland.
And it is perfectly logical to start the numbering of monarchs over again at one every time an old kingdom is abolished and a new one created.
The creation of the kingdom of Great Britain didn't affect the numbering since Queen Anne was the first and so far last Queen regnant named Anne, and the next three monarchs were the first British monarchs named George.
But when George III went to bed as King of Great Britain, Ireland, and France on December 31, 1800, and woke up as King of the United Kingdom of Great Britain and Ireland on January 1, 1801, he could logically have changed his number to George I.
Then George IV (1820-30) would have Been George II, William IV (1830-37) would have been William I, Victoria )(1837-1901) would have been Victoria, Edward VII (1901-1910) would have Been Edward I, George V (1910-1936) would have been George III, Edward VIII (1936) would have been Edward II, George VI (1936-1952) would have been George IV, and Elizabeth II (1952-) would be Elizabeth I, Prince Charles presumably Charles I instead of Charles III, Prince William William Ii instead of William V, and Prince George George V instead of George VI, and so on with as yet unborn generations.
With another twist, Queen Victoria of the UK (1837-1901), became Empress Victoria of India in 1876, and George VI gave up the title in 1948.
So if the UK monarchs were numbered as Emperors of India:
Queen Victoria (1837-1901) would be Empress Victoria of India (1876-1901)
King Edward VII or I Would be Emperor Edward I of India (1901-10).
King George V or III would be Emperor George I of India (1910-36)
King Edward VIII or II would be Emperor Edward II of India (1936)
And King George VI or IV (1936-52) would be Emperor George II of India (1936-1948).
It is always possible that in the future Wales, or Scotland, or Northern Ireland, or England, might become independent, turning the United Kingdom into a divided kingdom. And if that happens it might be considered logical to start the numbering of monarchs over again.
If Scotland becomes independent, the remaining country could be called the United Kingdom of England and Northern Ireland, and perhaps add Wales to the title. If that happens, a future King Robert or James of the United Kingdom of England, Wales , and Northern Ireland would be Robert the First or James the Third, while a future king Robert or James of Scotland would be Robert the Fourth or James the Eighth.
And it is possible that Scotland might become an independent Kingdom before there is another queen regnant named Mary. In that case the next Queen egnant of the kingdom that includes England (whatever name it might have) will be Mary III, and the next Queen regnant of Scotland will be Mary III.
And if Scotland continues to have the same monarch as the remnant of the UK (at the present time fifteeen other countries have the same monarch as the UK) Queen Mary III of the remnant of the UK and Queen Mary III of Scotland will be the same persons.
And if Scotland chooses to have a different monarch, there could be different Queens Mary the Third in the two countries at different times.
If Northern Ireland becomes independent, and maybe joins the Republic of Ireland or the USA, the United Kingdom might change its name back to Great Britain. And then it might be considered logical to change the numbering of monarchs back to Great Britain numbers, ignoring the numbers used by monarchs of the United kingdom. So under that system Prince Charles would be King Charles III, Prince William would be King William IV instead of William V, and Prince George would be King George IV instead of King George VII.
So even though precedents suggest that the next queen regnant named Mary in the British Isles will almost certainly choose to be known as Mary III, there is no legal need for her to be known as Mary III, and possible future events and/or her personality traits might make her Choose to be known as Mary I or Mary IV or some other number.