Not discussing how alternate successions to the crown could have gone; rather, what other names the monarchs that did reign could have taken.
A King of Queen can take either their first name, or a middle name. The current monarch, Queen Elizabeth II, uses her first name (Elizabeth Alexandra Mary). The first monarch to have a middle name, King James VI and I, used his middle name (Charles James). Every monarch since George I has had at least one middle name; there is a plethora of opportunities for alternate history here, even if only in the name used. The British monarchs, from Elizabeth I onward, with their reigns and full names, are:
1. Elizabeth I (1558-1603, England)
2. James VI and I (1567-1625, Scotland; 1603-1625, England) - Charles James
3. Charles I (1625-1649)
4. Charles II (1649-1651, 1660-1685, Scotland; 1660-1685, England)
5. James II and VII (1685-1689)
6. Mary II (1689-1694)
7. William III and II (1689-1702)
8. Anne (1702-1714)
9. George I (1714-1727 England; 1714-1715, 1716-1727, Scotland) - George Louis
10. James VIII (1715-1716, 1745-1746, Scotland) - James Francis Edward
11. George II (1727-1760, England; 1727-1745, 1746-1760, Scotland) - George Augustus
12. George III (1760-1820) - George William Frederick
13. George IV (1820-1830) - George Augustus Frederick
14. William IV (1830-1837) - William Henry
15. Victoria (1837-1901) - Alexandrina Victoria
16. Edward VII (1901-1910) - Albert Edward
17. George V (1910-1936) - George Frederick Ernest Albert
18. Edward VIII (1936) - Edward Albert Christian George Andrew Patrick David
19. George VI (1936-1952) - Albert Frederick Arthur George
20. Elizabeth II (1952-present) - Elizabeth Alexandra Mary
Assuming each monarch went by their first name, the list would instead be:
1. Elizabeth I
2. Charles I
3. Charles II
4. Charles III
5. James I and VI
6. Mary II
7. William III and II
8. Anne
9. George I
10. James VII
11. George II
12. George III
13. George IV
14. William IV
15. Alexandrina
16. Albert I
17. George V
18. Edward VII
19. Albert II
20. Elizabeth II
One of the more notable effects of this change is that the King James Version (KJV), authorised by King James VI and I in the early 1600s, would instead be the King Charles Version (KCV). One also wonders whether or not Jesus' brother Ya'akov's (Jacob) name would have been translated as "James" (i.e. we could've ended up with a "Book of Jacob" in the New Testament, rather than the "Book of James").
A King of Queen can take either their first name, or a middle name. The current monarch, Queen Elizabeth II, uses her first name (Elizabeth Alexandra Mary). The first monarch to have a middle name, King James VI and I, used his middle name (Charles James). Every monarch since George I has had at least one middle name; there is a plethora of opportunities for alternate history here, even if only in the name used. The British monarchs, from Elizabeth I onward, with their reigns and full names, are:
1. Elizabeth I (1558-1603, England)
2. James VI and I (1567-1625, Scotland; 1603-1625, England) - Charles James
3. Charles I (1625-1649)
4. Charles II (1649-1651, 1660-1685, Scotland; 1660-1685, England)
5. James II and VII (1685-1689)
6. Mary II (1689-1694)
7. William III and II (1689-1702)
8. Anne (1702-1714)
9. George I (1714-1727 England; 1714-1715, 1716-1727, Scotland) - George Louis
10. James VIII (1715-1716, 1745-1746, Scotland) - James Francis Edward
11. George II (1727-1760, England; 1727-1745, 1746-1760, Scotland) - George Augustus
12. George III (1760-1820) - George William Frederick
13. George IV (1820-1830) - George Augustus Frederick
14. William IV (1830-1837) - William Henry
15. Victoria (1837-1901) - Alexandrina Victoria
16. Edward VII (1901-1910) - Albert Edward
17. George V (1910-1936) - George Frederick Ernest Albert
18. Edward VIII (1936) - Edward Albert Christian George Andrew Patrick David
19. George VI (1936-1952) - Albert Frederick Arthur George
20. Elizabeth II (1952-present) - Elizabeth Alexandra Mary
Assuming each monarch went by their first name, the list would instead be:
1. Elizabeth I
2. Charles I
3. Charles II
4. Charles III
5. James I and VI
6. Mary II
7. William III and II
8. Anne
9. George I
10. James VII
11. George II
12. George III
13. George IV
14. William IV
15. Alexandrina
16. Albert I
17. George V
18. Edward VII
19. Albert II
20. Elizabeth II
One of the more notable effects of this change is that the King James Version (KJV), authorised by King James VI and I in the early 1600s, would instead be the King Charles Version (KCV). One also wonders whether or not Jesus' brother Ya'akov's (Jacob) name would have been translated as "James" (i.e. we could've ended up with a "Book of Jacob" in the New Testament, rather than the "Book of James").