If the Anglo-Saxons were so prominent then why is Great Britain a term we use? Doesn't this reflect older, less "cool" roots towards Wales, Brittany and ultimately Ireland and Scotland?

hi! I'm not entirely clear on this question, but you might get something out of these posts which discuss the term "Great Britain".

I'll just point out, because I don't think this comes up in the threads, that Great Britain can be an ambiguous term. To start with, it is a geographic term: the name of the largest island in the British Isles island group. Then, since the bulk of England, Wales, and Scotland are all located on that island, Great Britain can be a political term referring to all three as a unit. Following on from that, the term can be used even more loosely to refer to the entire United Kingdom of Great Britain and Northern Ireland (the UK).

When and how did Britain get so great?
Where did Great Britain get its "Great" from?
To what extent would 'England' and 'Great Britain' (or the UK) have been synonymous terms during the period of the British Empire?