Poetically, often known as "Erin". Politically, formerly known as "Eire". In Irish mythology, the goddess of Ireland was known by three names relating to her triple-aspect - "Eriu", "Fodhla" and "Banbha". There are also the nicknames, "The Emerald Isle", "The Auld Sod" and "The Island of Saints and Scholars. Hopefully one of these is what you're looking for!