I have taken your advice and looked at the etymology of "Britain", "Great Britain", "United Kingdom" and "United Kingdom of Great Britain and Ireland / Northern Ireland".
First "Britain". It is derived directly from the Roman name, "Britannia". This was the name they used for that part of the British Isles that they occupied. This was today's England and Wales south of the border they constructed, Hadrian's Wall. The Wall is located on today's border between England and Scotland .
Now "Great Britain". It was first used when King James
VI of Scotland was crowned King James I of England on 25 July 1603. It was used to signify that a single monarch now ruled two kingdoms, the Kingdom of Britain and the Kingdom of Scotland.
Next "United Kingdom". It was first formally used on 22 July 1706 in the Treaty of Union between the British and Scottish parliaments. The United Kingdom of Great Britain came into being when the Act of Union was passed by both the Scottish and British parliaments on 1 May 1707.
Now for "United Kingdom of Great Britain and . . . ". This was first used in the form "United Kingdom of Great Britain and Ireland" in the Act of Union of 1801 that bought Ireland into the family of nations. In 1922, when the Republic of Ireland gained its independence it was changed to "United Kingdom of Great Britain and Northern Ireland'.
So if Scotland votes 'Yes' in theory:
Great Britain is redundant
Britain and British Airways remain unaffected
The 'United Kingdom of Great Britain and Northern Ireland' might be officially renamed the 'United Kingdom of Britain and Northern Ireland'.
None of this stops the likes of Wikipedia from trying to tell us that Scotland is part of Britain or that Britain is an island (when it is joined to Scotland that is not part of Britain) or, indeed anyone who has not reseaced the background from saying something different.
What is of particular interest is that the name "Britain" is older than the name "England". Note that "England" is a corruption of the words "Angle Land". It followed the invasion of eastern Britain by the Anglo Saxons starting around 450AD only some 40 years after the Romans left Britannia.