While you're right that it is called that (by many), some people object to it:
> In Ireland, the term "British Isles" is controversial, and there are objections to its usage. The Government of Ireland does not officially recognise the term, and its embassy in London discourages its use. Britain and Ireland is used as an alternative description, and Atlantic Archipelago has also seen limited use in academia.
I'm Irish and I've always found the controversy a bit ridiculous; it's a classic example of Irish people's distaste for all things English being taken to a nonsensical extreme. You never hear Brits complaining about the Irish Sea being called such.
I don't know, given the Isle of Man is in the middle of it, maybe it should be The Manx Sea? If we don't want anyone to own it, maybe call it The Sea of Sodor?
A similar controversy exists in the Arab world about what to call the Persian Gulf, where the names "Arabian Gulf" or simply "The Gulf" are preferred. [1]
Amusingly (but perhaps not surprisingly), British imperialism briefly waded into this dispute as well:
> Following British attempts to control the seaway in the late 1830s, the Times Journal, published in London in 1840, referred to the Persian Gulf as the "Britain Sea", but this name was never used in any other context.
I guess that's reasonable, though it appears the name goes back to the 1st century, so the UK is named after the Isles, rather than the other way around?
Great Britain may have been named after one of the isles, but the controversy arises because the UK spans (part of, but not all of) the two main isles.
> Has anyone proposed a viable alternative?
I don't know what would count as "viable" if you reject "Britain and Ireland" and "Atlantic Archipelago".
> Great Britain may have been named after one of the isles
Great Britain is the largest island of the isles. The UK's full name is The United Kingdom of Great Britain and Northern Ireland; ie there's no political entity of Great Britain (and never has been).
No, I don’t think you can fairly say a country is an archipelago unless it’s solely composed of islands all of which are entirely the territory of that state.