One nice feature of this name is that the acronym IONA has the same spelling as the island of Iona which is off the coast of Britain but which Irish people have strong cultural association. It is a name with which people of both main islands can identify. However, it has the problem that Iceland and Newfoundland, to name just two, are also islands of the North Atlantic.
References:
[1] Denis Canavan MSP, British Irish Inter-Parliamentary Body, Summary of the 15th Plenary Session, 9. The Future of the Body
[2] Trevor Sargent TD, "The Good Friday Agreement", Dail speech
[3] Mr. Peter Luff MP, House of Commons speech
[4], Kevin Barry, "Resiliency, Tolerance and Avoidance in Northern Ireland"
[5] Taoiseach Mr Bertie Ahern TD, "Ireland and Britain A New Relationship for a New Millennium"
[6] Paul Sharp, "When New Meets Old: Irish Diplomacy, Northern Ireland and the Peace Process"