Land of the "Pritani" if you go back to Pytheas of Massilia 2,400 years ago. Hence latinised by the Romans into Britannia and thus to British.
It was King James VI of Scotland and I of England who promoted the term Great Britain in pursuit of his aim to unite the two Crowns from a personal Union into one country. That did not happen until the joint Acts of Union of 1707 under Queen Anne. So that is only 450 years ago and the understood Lesser Britain being Brittany (Bretagne or Breizh) which was settled by Britons fleeing the English invading across the North Sea and is now part of France.
However in Roman times the assumption was that the Lesser Britannia was a reference to the smaller island of Ireland across the Irish Sea. The first name the English gave the larger island was Breoten when they arrived there.
It is all quite simple. One country, four nations, three Crown Dependencies and eight languages (Irish Gaelic, Scots Gaelic, Scots, English, Cornish, Welsh, Manx and Anglo-Norman French) now that Norwegian based Norn is extinct. The nearest language to English is Frisian and not one of the native languages. Constitutionally (but not actually) reigned over by Charles III as King of England and Wales, of Northern Ireland and of Scotland, Lord of Mann, Duke of Normandy of the Bailiwick of Jersey and of the Bailiwick of Guernsey.
But one can choose any of these names for the whole island or extended as the United Kingdom as far as I am concerned but England should be reserved for the nation of England itself.
However I have bored the good people of the forum into a near-death experience enough. So I will leave the subject alone.
Bledhen Nowydh Da.