Íverin was the name of an island to the west of Tol Eressëa after its breaking during the Faring Forth, according to the early version of the legendarium in The Book of Lost Tales. The island later became known as Ireland.
In the Faring Forth, a great expedition by the Elves of Tol Eressëa for the rescue of their kin in the Great Lands, the island of Tol Eressëa was dragged across the Ocean from the West, and anchored near the shores of the Great Lands.
The Vala Ossë, angered at the uprooting of the island that he himself has set in its place in the West ages ago, attempted to drag it back to Valinor. However, the island broke apart, and the western portion of what was once Tol Eressëa became its own island, which the Elves named Íverin, but which would eventually be called Ireland by Men.