Since the devolution process began in the nineties, there has been some genuine traction for the name of the archipelago to be changed to 'Iona'. Which is quite elegant: The name of a Hebridean island, a pre-Norman, dual culture monestary and the triple whammy of standing for Isands Of the North Atlantic.
This idea has been rattling round for a while, mainly in Dublin and Stormont, wary of British dominace understandibly, but it has it's fans in Holyrood and Cardiff too. I have a feeling it may been voiced in Westminster, but I'm not sure.
It's also never going to happen, considering that it's a pretty fringe suggestion even among the Welsh and Scottish nationalists (and a minority of the Irish in Stormont), who are themselves minorities within Wales, Scotland and, slimly, Northern Ireland, who are themselves significantly outweighed in voting power by England, where it's even more of a fringe movement. Ireland may attempt to do it themselves for official maps and so forth, but even then I doubt it would get much traction.
Not to mention that it'll never be used academically, as it excludes the other islands of Greenland, Iceland, the Faeroes, Newfoundland etc. and
includes Great Britain, the Isle of Man and the Channel islands which aren't even in the North Atlantic. Indeed, the only official organisation to use it includes these islands as part of the grouping.