I just call it "England".
But that's rather like calling the Netherlands "Holland." Lots of folks do it, even a few cartographers, but in Netherlands Holland refers only to two provinces, Noord Holland and Zuid Holland, within the Netherlands. England is sort of like that. It's only part of the larger of the islands.
I think it's an interesting question, and one that I hadn't even thought of. I'm not sure that I have ever referred to the British Isles by any name, but when I saw the question British Isles was the name that immediately came to mind--well, British Aisles came to mind, though I cannot remember why--making me think that this is the commonly-used term in the English Language. After voting, I surfed into the same Wikipedia article posted later by politicus and saw that it's actually an ancient name, and one that predates the English language by several hundred years. It should not be surprising, therefore, that it is overwhelmingly the option chosen by the voters herein.
According to that same article, "these islands" is the preferred phrase among some nationalists in Northern Ireland as well as in in documents drawn up jointly between the British and Irish governments. Makes sense. Outside Ireland, however, I think the phrase British Isles must be overwhelmingly preferred, as is evidenced by this poll.
The third option in the poll is unnecessarily ambiguous. The second option is logical, but it is not the one that has been popularized. Also, it has the disadvantage of losing Ireland. People get tired of saying "this and that" and it invariably gets shortened to "this" only. I don't know anyone from "Trinidad and Tobago" but I have met several people from Trinidad. I don't know anyone who has ever gone scuba diving in Saint Vincent and the Grenadines, but I know many who have been to Saint Vincent and a few who have visited the Grenadines. People from São Tomé e Príncipe are invariably called São Tomean, and not São Tomé e Príncipeans.
I guess you could avoid that by putting the more populous one last. If it was called Príncipe e São Tomé then they'd both stick. Same with Ireland and Britain. Folks aren't going to leave off Britain. So that might also be a reasonable poll option, though I still don't think it'd steal many votes away from the well-established name that seems to be winning.
For example, Provo, which is in the Caicos, has more people than any of the other islands in Turks and Caicos, including Grand Turk, so nobody just says "Turk." Then again, when people visit Provo they just say Provo. "Where'd y'all go?" "Provo." "Really, sweet. Um, where's that?" "Turks and Caicos islands." "Oh, where's that?" "Near Cuba. Sort of."
Poll
