The noun Éire is a little exceptional in how it combines with the definite article. Even though it never has an article in the nominative (Éire) or in the dative (in Éirinn, go hÉirinn etc), it can optionally have it in the genitive. So Éireann and na hÉireann are both grammatically correct genitives of Éire. Sometimes the choice of one over the other can be meaningful. The articled genitive is felt as introducing a greater degree of semantic definitiveness to the whole noun phrase. So if uisce Éireann could be paraphrased as water of Ireland, uisce na hÉireann would be the water of Ireland.

In standard Irish Éire is the nominative case and Éirinn is the dative case. That is why we say tá Éire go hálainnIreland is beautiful but tá sé go hálainn in Éirinnit is beautiful in Ireland. In some dialects, however, the form Éire does not exist and Éirinn functions as both a nominative and a dative.