Why is the current reigning monarch called "Queen Elizabeth II" (read details before answering)?

Only Queen regnants (monarchs in their own right) are numbered.

Queen Elizabeth, the Queen Mother was a consort (the wife of King George VI) so she never got a number. There have been several queens of England/UK called Elizabeth, but only two have been sovereigns. Henry VII's wife was Queen Elizabeth as was Edward IV's wife, both consorts. On your reckoning the present queen would be Elizabeth V.

The Tudor Queen Elizabeth was never the monarch of Scotland, so as far as the Scots are concerned the present queen should be Elizabeth I (Robert the Bruce's consort was also Elizabeth but again not queen in her own right) but the numbering of Scots kings and queens has always been a bit odd hence James I of England was also James VI of Scotland and William II in Scotland was William III in England. The present queen settled on Elizabeth II as being the least confusing option.

Queen Elizabeth II is the SECOND Queen Regnant named Elizabeth. A Queen Regnant is a female Monarch who reigns in her own right.

Queen Elizabeth II's mother, also named Elizabeth, was not a Queen Regnant - she was not a reigning Monarch. She was Queen Consort to the King Regnant of the UK during his lifetime. She was the wife of the King, and for that reason she was known as Queen Elizabeth. Upon his death, her proper title and style was Dowager Queen Elizabeth (the widow of a King).

Only the reigning queen, a Queen Regnant, bears the ordinal number after her name.

There are different types of Queen:

Queen Regnant, the hereditary monarch who has powers to reign

Queen Consort, the wife of the reigning king; a consort does not have hereditary powers to reign

Queen Dowager/ Queen Mother, the widow of the king

There have been only two Queens Regnant named Elizabeth, Elizabeth of the Royal House of Tudor, and Elizabeth II, of the Royal House of Windsor.

The Queen's mother was only the consort. She was married to George VI, who was the reigning, hereditary king. The former Lady Elizabeth Bowes-Lyon was not the heir to the throne of George V. As a wife, she was able to assume her husband's titles and styles, but not his hereditary powers. She could not be the regnant queen as she was not the heir.

Just to clarify a little, since you've received some good answers: there are two kinds of queen, queens regnant and queens consort. A queen regnant is a woman who reigns in her own right, having inherited the throne from a blood relative who was the previous monarch. Queen Elizabeth I and Queen Elizabeth II are queens regnant.

A queen consort is merely the wife of a king. She does not have any reigning powers and therefore, as other posters said, she does not receive a regnal number. She is not the monarch. Elizabeth II's mother, the late Queen Mother, was a queen consort.

The only real issue, therefore, has involved the Scottish view, described by another poster, that Elizabeth II shouldn't use that numeral in Scotland, because the woman called Elizabeth I never reigned in Scotland.

From the accession of James I to the throne of England, the numbering system for the monarchs of England and Scotland were different until the Act of Union in 1707. James I was James VI of Scotland, Charles I and Charles II were the first and second Charleses in each country. James II was James VII of Scotland. Mary II was Mary II in both countries, (Mary Tudor was Mary I in England while Mary Queen of Scots was Mary I in Scotland). Mary II's husband was William III in England and William II in Scotland and Anne was just Anne in both countries. After the Act of Union, Scottish numbering was ignored. William IV should have been William III; Edward VII and Edward VIII should have been Edward I and Edward II; and Elizabeth II should have been Elizabeth of Scotland. The Scots only really grumbled about Elizabeth. They must have forgotten the Edwards.

Only monarchs who have ruled England/Britain since William I in 1066 get numbers. And not all of them either. As well as the accepted canon, Matilda (daughter of Henry I, mother of Henry II) ruled England for a few months in 1141 when she captured her cousin King Stephen during the civil war known as the Anarchy. Henry II had his son, Henry crowned King while he was still alive. He was known as Henry the Young King and would have been Henry III except that he died before his father and his brother Richard I succeeded. Jane Grey was declared Queen in 1553 on the death of her cousin Edward VI but Edward's half sister Mary rallied support and locked Jane up in the Tower, later to be beheaded, after she had ruled for nine days.

Elizabeth II's mother was never queen in her own right, she was titled queen because she married george VI, but she was his queen consort, numbers to queens are only given if they reign in their own right, so our present queen is elizabeth II because we have already had an elizabeth I.