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.

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.

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.

However, note that Churchill (and the Queen) was careful not to seek to bind future monarchs in this matter.

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.