There was some discussion about the modern name of the English civilisation, and a lot of the information was wrong (and some was even ridiculous).

I've studied a fair amount of history, so here are some explanations.
There are two main islands, and a lot of small ones, that make up the British Isles. The main islands are:
1 Great Britain
2 Ireland
The name Great Britain comes from the Roman name of the island, and has nothing to do with the British Empire. The Romans called the island 'Britannia', but there was a lot of migration between Britannia and Armorica in north-west Gaul, especially after the fall of the Roman Empire. Because of this migration, 'Britannia' eventually came to be associated with both places. They were therefore distinguished by calling the island 'Britannia Major' and Armorica, which was much smaller, 'Britannia Minor'. These names mean 'big Britain' and 'little Britain' in English, which is exactly what 'Great Britain' and 'Brittany' mean too.
'Great Britain' and 'British' were first used officially after the English and Scottish parliaments voted to unite England and Scotland in 1707. A new name was needed since the new Kingdom was neither England nor Scotland, so the name of the island was used. The official name was 'The United Kingdom of Great Britain', and 'Great Britain' was the normal short form.
When the Irish parliament voted to join with Great Britain in 1800, 'Great Britain' ceased to be an accurate short name for the combined kingdom. This is still true, because Northern Ireland voted against leaving the UK when the rest of the island did. The normal short form of 'The United Kingdom of Great Britain and Northern Ireland' (or 'The United Kingdom of Great Britain and Ireland' in the past) is therefore the 'United Kingdom', and not 'Great Britain' or 'Britain', but 'Britain' is better than 'Great Britain', since it isn't the name of one of the islands.
'British' can still be used to mean the people of the island of Great Britain, but the normal usage means the people of the United Kingdom, including Great Britain, Northern Ireland and the smaller islands. This refers to the geographical connexion between the British Isles and the United Kingdom, i.e. that all of the islands that make up the UK lie within the British Isles.
Based on the above, the countries/nationalities of the British Isles should be:
1 The United Kingdom / British
2 Ireland / Irish