Pertinent but fairly meaningless. Ireland and the United Kingdom are seen as one passport and customs free area currently. An independent Scotland is unlikely to change that.
Never say never and never claim to be able to predict the future. Although the current rules on accession of new members seem to be rigid, it is surprising what a few months of negotiation can do. Same for the negotiations with the Rump UK- lots of big talk now, but when real politick starts, concessions will be made.
The Evolution of the name of the country has been:
England (England and Wales geographically but referred to as England)
The United Kingdom of Great Britain (same monarch for England and Scotland)
The United Kingdom of Great Britain (loss of Scottish Parliament)
The United Kingdom of Great Britain and Ireland (integrating Ireland)
The United Kingdom of Great Britain and Northern Ireland.
Great Britain is the geographical area of Scotland, England and Wales
GB technically does not include NI even though it is the usual abbreviation for the Olympics etc.
Britain has been used informally since the 1970’s to refer to the UK (the lesser being larger than the greater!)
I suggest Little Britain if no-one else has used the name.
Seriously though, even after separation it will still be the United Kingdom (Queenie will be shared directly as one monarch, unlike in her other realms where technically the Queen of Canada is separate from the Queen of the UK.) Just that there will be two separate political and independent entities making up that Kingdom.
Yeah, but no, but yeah.
Quibbles:
You’re treating the Kingdom of England as the predecessor state of the UK, but not the Kingdom of Scotland. The Scots would dispute that! Your first line should treat England and Scotland as distinct and equal entities.
Plus, during the period (1603-1707) when the Englishn and Scottish thrones were occupied by the same person, there was no “United Kingdom of Great Britain”. The King of England and Scotland was occasionally referred to as the King of Great Britain, but there were still a distinct Kingdom of England and a Kingdom of Scotland.
Plus, from 1707 to 1801, the formal title of the country was the “Kingdom of Great Britain”, though it was often referred to as the united Kingdom. I don’t think it formally became the “United Kingdom” until Ireland was incorporated in 1801.
It has been used a lot, at various times, to refer to (a) Wales, (b) Cornwall, (c) Brittany or (d) a humorous radio, and later television, programme.
Well, that remains to be seen (or decided). But referring to two independent countries with their own governments, parliaments, etc as a “United Kingdom” on the grounds that they shared a monarch would be a novelty. Prior to 1801 Britain and Ireland had exactly the same “single monarch” relationship as I think you envisage for Scotland and rump-UK, but they were never referred to as a “United Kingdom”.
If I can speak for Ximinean, the England teams of all major sports traditionally feature blue as an accent colour - eg in the vest of. the three lions, the socks (rugby and football), shorts (football), maybe stripes or collar details. Prior to the 2013 season, the England & Wales cricket team wore navy blue for T20 and ODIs, and will do do again, no doubt, when the ECB want to sell a few more shirts.
Blue features often more frequently than red, which often isn’t used at all.
Fascinating factoid of the day: blue sportsgear sells better (as leisurewear) than sportsgear of any other colour.
Which is why lots of teams that don’t have blue as their primary strip have adopted it as their alternate or training strip, or are working as much blue accent as possible into their primary strip. Or have even changed their primary strip.
The English representative sports teams are no exception to this. But nor is it something distinctive to them, such as would justify identifying blue as somehow representative of England in the sporting world. The fact is that so far as sporting colours go, blue is very strongly associated with Scotland, so choosing it for a flag intended to designate the-UK-without-Scotland on the basis of its being somehow distinctively English is not very convincing. English teams wear white.
Already taken (why do you think Britain is called “Great”?). Little Britain (Britannia Minor) is Britanny, in France.
England cricket team crest
England football team crest
Blue has been a feature of English sports team strips for decades. Of course blue is synonymous with Scotland, but they aren’t the only ones allowed to use it. No one is suggesting that blue is representative of England over white and red, but that doesn’t mean it can’t be an accent colour, in a flag or anywhere else. Anyway, if our Monarch would consider restaking her claim to france, we could happily keep the blue much favoured in the old royal coat of arms of England. 
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But we digress. It would make more sense feature the Cross of St David, for the Welsh. This is actually pretty cool(YouTube link).
It would still be the United Kingdom, but Scotland would no longer be a part of the Union. Just as the United States would still be the United States, if the southern confederacy seceded.
Yeah, but the United Kingdom of what is the main point of the discussion. ‘Great Britain’ specifically refers to the largest island within the British Isles, which includes Scotland.
My vote is for the United Kingdom of England, Wales and Northern Ireland. Keeps everyone happy, doesn’t piss off the Scots. Well, part from Irish nationalists, but we’ll save that for another day.
To expand on SanVito’s point, it’s only a united kingdom because of Scotland. Wales and Northern Ireland are effectively conquered holdings. Scotland and England were (nominally) united by the accession of James I/VI to the throne of England.
“United Kingdom of Southern Britain and Northern Ireland”
Sounds straightforward to me.
Or it could just be the United Kingdom of Britain and Northern Ireland. Great Britain is the whole island, but Britain is just the political agglomeration largely dominated by England.
However, Wales has had a couple of kings, historically (Hywel Dda and Rhodri Mawr), and Northern Ireland can be seen as the successor of the medieval Kingdom of Ulster (Ulaid). So it could be a unity of those three kingdoms. Or a unity of the kingdoms of the medieval Heptarchy. Or anything, really.
What I want to know is why Scotland won’t take Northern Ireland with it. England conquered Wales before the union; no reason to split that (well, not in the context of Scottish independence, anyway). But the Northern Ireland plantations occurred before unification, and most of the settlement was from Scottish rather than English Protestants, as I understand it. Because of the power imbalance, most of the anti-British ire is toward the English. I’d like to see Scotland take N. Ireland with it when it splits, and England and Wales go their own way.
I know the chances are nil, but it’s interesting how unthinkable it is given the history.
Ooh, I likey.
Or we redefine what the ‘United Kingdom’ bit means: a single Kingdom that unites three countries under one Monarch.
Now here’s a plan, ladies and gentlemen! Solves all sorts of difficulties in one. If we really wanted to upset the Welsh, we could just revert to being ‘England’ as we were before the Union and sod the United Kingdom bit.
Let’s start a campaign…
You could call it Wengland.
Given that the National average lifespan would increase, along with a reduction in average smoking, drinking and pie-eating I would say ‘Long Live the Queen and her subjects’
If that’s what we go with then I expect you to support my campaign to be in the BBC’s next list of 100 Greatest Britons or whatever it’s called. I’m still a citizen and everything. 