I'm inclined to to think that the Barclays Premier League is an English League and part of the English Pyramid System. This has some Welsh clubs, with Swansea having been there from almost the beginning. But apart from the few Welsh clubs in the system there is no way for other Welsh teams to enter the system via promotion.
If a team from Poland joined the German League, we'd all still call it the German League. We wouldn't call it the German and Polish League.
I think the Barclays Premier League is an English Premier League that allows a few select Welsh Clubs in it. It may also allow Celtic and Rangers one day.
Just because Swansea are there doesn't suddenly make it non-English. Swansea is just the exception.
The reason it is called the Barclays Premier League and not the English Premier League is for sponsorship reasons. Barclays want people around the world to link their name with the league. But if you're trying to promote the Premier League in Asia and other regions, where no-one has heard of Barclays, then the fans there will call it the English Premier League, because Barclays is meaningless to them.
It couldn't be called the English and Welsh Premier League, because Wales has it's own Premier League (it might be called something different).
I will probably cop a lot of flak for this, but just think about it from the position of someone who's neither English or Welsh? It is clearly an English League system that has a few Welsh teams. And I think the Welsh system has one or two English teams.
Should Welsh teams be allowed to play in it? Of course they should. Because the Barclays Premier League and English Pyramid System doesn't have any rules that bar teams from outside England. Even a French team could play in it.
This should be about football, not petty nationalism. Any great league should want the best teams playing in it. And at the moment Swansea are one of those best teams.