- First, the Scots are an ethnic group. That's right, they actually are a group of people that migrated to Scotland from Ireland in the fifth and sixth centuries. They founded a kingdom along the Western Isles called Dal Riata and eventually conquered/merged with the indigenous people of Scotland—or more appropriately, Alba—the Picts. Second, the ruler of Scotland was never truly the "King" or "Queen of Scots" because the nation was multinational. It included Scots, Picts, Norwegians, Anglo-Saxons, and Britons. The united kingdom by around 800 was quite multiethnic and multilingual. After the Norman Conquest in 1066, many French and Norman settlers found homes in territories that would soon fall into the Scottish fold.
- Second, there are a lot of modern-day immigrants to Scotland that would not even remotely consider themselves "Scots" such as Africans, Indians, Asians, and the English. None of these would really be "Scots" so naming Elizabeth such would alienate them.
- Third, some may argue that "Scot" is more a political term than an ethnic term. I disagree. "Belgian" is a political term. Belgium did not exist until 1830 and really has no roots in, well, anything. It is a political construct. For that matter, "Niederlander" (a person from the Netherlands) is also a political term since that nation came up the same way and the term simply means "Low Lander" anyway. "Scot" refers to a very specific ethnic group from which the royal family derived. Elizabeth certainly has some Scots blood. Heck, she even has the "Scot" blood, but it would serve her well to not call it out anyway. There are a lot of non-Scots in Scotland.
- Fourth, "Queen of Scotland" just makes sense. It's a geographical area that is internationally recognised. No one would really dispute its existence. People who are citizens of Scotland would be "Scottish" because that's the name of a citizen. Notice, it's not "Scot". That's because Scots are an ethnic group. The Scottish are a geopolitical entity. There is a difference. I could never be a Han, a member of the dominant Chinese ethnic group, but I could become Chinese if I became a citizen of China (or Taiwan). One is an ethnic group, one is a geopolitical entity.
- Finally, Scotland really needs to redefine itself if it gains independence. Falling back to "Queen of Scots" would be trying to reverse 307 of union with England. That can't be undone, I hate to tell you. Scotland and England have been joined for three centuries and no revision of history will successfully deny that. Heck! Both countries technically ceased to exist—they became "Great Britain" and later the "United Kingdom" once Ireland got in on the game (read was forcibly coerced with threats of violence). Scotland is the modern entity. There is no need to go back three hundred years and try to start where you left off. There are reasons you unified back then. Remember?
On some further points regarding the queen and Scottish independence, let's bring up her regnal number: II. Queen Elizabeth is the second Elizabeth to rule England. When England and Scotland unified in 1707, it was decided that monarchs would take the next number from either the English or the Scottish lists of kings and queens, whichever number were higher. Thus a King Henry would be Henry IX rather than Henry II, as he would have been in Scotland. Meanwhile, King Malcolm would be Malcolm V rather than Malcolm I as he would be in England. This system, so far, has only be used four times, once with William IV (he would be William III of Scotland), twice with Edward VII and Edward VIII (who would have been Edward I and Edward II of Scotland, claims of Edward Balliol notwithstanding), and once with Elizabeth II (who would be Elizabeth I of Scotland). As can be seen, Scotland has been shafted with none of the British monarchs continuing the Scottish numbering. Neither England nor Scotland had its own Georges or Victorias, and all the Jameses came before the Act of Union in 1707 so have both numbers. Elizabeth has kept her II in the British Commonwealth, but Scotland may choose to reverse the Act of Union by renumbering her Elizabeth I, thereby confusing history students forevermore. We'll see, I suppose.
Then there is the succession to consider. Scotland would naturally want to keep Elizabeth as its queen, assuming they choose to stay in the Commonwealth or keep a monarch at all. Either situation is possible, though Elizabeth does so love her Holyrood Palace in Edinburgh. .:.sigh.:. Anyway, technically Elizabeth isn't really the heir to the Scottish throne, though. There are various claimants with arguably better rights. First, there is the Jacobite claimant, Franz, titular duke of Bavaria. He has a brother, Max-Emanuel Ludwig Maria, and a niece, Sophie Elisabeth Marie Gabrielle of Bavaria, who is married to the crown prince of Lichtenstein. Together, these three individuals have the senior genealogical right to the throne as successors of James II who was deposed in 1688 in the Oh-So-Overglorified Revolution that saw England briefly conquered by the military dictator of the Netherlands, William of Orange. To be honest, though, they aren't going to rule in Scotland unless some dynastic marriage brings the families together again (hook Prince George up with Sophie's future child!).
The better contender is actually the senior heir to the house of Hamilton, the family that was next in line to claim the Scottish inheritance after all other Protestant families were eliminated from the succession. The first family was Sophia of Hanover's. Her son inherited Great Britain in 1714 after Anne died and just a few months after Sophia died. The Scots tried desperately in 1704 to bypass Sophia and go for the next heir via the Act of Security, but the heir, James, 4th Duke of Hamilton, wasn't really interested in the title and there were no other Scots with a decent claim to the throne alive. It was a rather disappointing situation. When the Act of Union was voted on in the Scottish Parliament in 1707, James absented himself claiming to have the sniffles. His senior heir, according to British succession standards, is a bit difficult to pinpoint, but the dowager duchess of Hamilton, Kay Carmichael, supports independence just for the sake of Scottish identity. Smartly, the actual Hamilton heir, Alexander, 16th duke, has not made a statement
I should go back and show a bit of a progression of royal arms in England and Scotland.
England began in 1603 with three lions resplendent in the top-right and bottom-left quarters with fields of fleur-de-lis in the opposite corners. This reflected the two proclaimed realms of England: England and France. Wales was subsumed into England as a territory, so had no independent status, while Ireland was a lordship until the 1530s and afterwards was a client kingdom. The fleurs-de-lis got reduced to simple trios in 1406, but remained until 1800.
Meanwhile, Scotland's flag went relatively unchanged for four hundred years until the physical merger of the crowns in 1603 under James VI/I.
Things got complicated under James I. He wanted to properly represent all his kingdoms, so added Scotland and Ireland to the grid. That sent the old English/French flag to the corners. But he kept them quartered within their two quarters, so we get little mini arms everywhere. The French claims were still maintained during his reign, so they stayed on the arms.
After the 1707 act of union, Scotland and England became united, so they moved Scotland into the quarters with England, and pulled France out to be its own quarter again. Bloody nice of them since France had its own secure monarchy for about 250 by that date.
The Hanoverians in 1714 switched out the bottom-right corner to put their own German territories on the arms, but I'm not going to bother putting that one up since it doesn't matter here.
In 1801, Ireland joined the union as the third kingdom of the "United Kingdom" with the name "Great Britain" becoming reduced to a component of the longer name. At the same time, all claims to France were finally dropped since France wasn't even a kingdom in 1801, it was a republic. Thus England and Scotland got their own quarters again. And just to be nice, in Scotland, the Scottish lion gets the two quarters and England takes the one.
An independent Scotland would once again screw up heraldry but getting knocked off the royal flag. In fact, Britain may well boot Ireland off too since the remaining bit, Northern Ireland, isn't even legally a kingdom so doesn't really belong on the flag to begin with.
That brings me to my last point. An independent Scotland means an independent England. The United Kingdom would be over officially (rather than its unofficial breakup after most of Ireland seceded) and England's claim to being "Great Britain" would end. England would be England again (with that Welsh bit still hanging on) and Scotland would be Scotland again. Ireland is a bloody bugger of a confusing state, but that's a different rant. With the breakup of 307 years of union, both countries would have to enter the world anew. England would retain residual rights over many international things, but both states may have to reapply for entry into organisations and legal names may have to change. For the Conservative Party in England, they will also lose their coalition and the country will vote and replace them.
Many things may change with Scottish independence and not all of them are good. Scotland is an ancient kingdom but it will be better off as a part of Great Britain. It doesn't lose its heritage in either case, that's something that globalisation will inevitably do. If you can vote, vote no because Scotland will truly revert to a time before England would come and save it, and that's not good for anybody.