It's not a British Isle -- it's an Irish one. Great Britain refers to the main island composing England, Scotland and Wales. The Irish isle of Ireland is composed of the two Irelands (Ireland and Northern Ireland). The 'British Isles' term is disputed by many Irish people. The reason it's not a geographic term is because it's not a river -- Britain is a geopolitical entity not a purely geographic one.
The fact the Ireland was head of the GDPR for the EU was merely an odd coincidence and has been rectified. You won't many upset Irish people over this.