Eg, United is the only STAR member in the states, Air Canada is the only STAR member in Canada, SIA is the only STAR member in Singapore, ANA is the only STAR member in Nippon, Mexicana is the only STAR member in Mexico,....you sense a pattern here. In fact every STAR member holds the exclusive "STAR" designation in their respective country. So I don't what you or BD was trying to get at.
#2, we all alliances change, form, dissolve etc.. Why tie in the airline's complete image and identity with something far from immutable.
#3, Also, is the airline ailing so greatly, that its STAR affiliation is being banked on as a complete saving grace to reinvigorate the carrier? Nope. In fact no other member in STAR or any other airline for that matter has decided to incorporate its alliance into its name.
So the name UK Star, while sounding boring and cliched, seems to have little logic.
Let me just say, that British Midland, while a fine carrier, is no British Airways. Whether BA is the world's favorite airline is debatable, but that it is one of the world's most important and active is not. BA is one of Britain's most recognized national symbols abroad, and a former state enterprise that has a history of representing HRH around the world. Any tinkering or deBritishization of this national pride symbol (depsite its recent difficulties) of course was taken with nothing but skepticism. British Midland does not fit this bill in the least. Its preposterous to think that if "British" was removed from the title, anything in the neighborhood of the BA disaster would ensue.