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).
Has anyone proposed a viable alternative?