All of our monarchies were unified under one king called James, the Scottish king in the early 1600's, the laws are the Union of Crowns 1603 and then later the Act of Union 1707.

Britain was a mixture of Scottish, English and Welsh aristocracy and later the Northern Irish after the plantation of Ulster that decided to work together.

We were not conquered by a group of British people that lord it over us. When we all became United as one people we chose the term British.

The word British comes from the Roman name for us Britannians, which come from one of the Welsh names for their people Brythonic and now it's the Britons.

You seem to have this idea that British name is not ours but it's a bunch of people that rule over us.

That's not the case it simply is that when we United the four different peoples of our islands we chose a name to collectively call ourselves.

We still mention the Scottish English etc in day to day life, and have our own individuality but when were talking about about all of us we use the term Britain.