If you’re using English, it’s Ireland. As Gaeilge, it is Éire, not Eire (or Éireann, depending on the grammar, but in this context the former version would be used); referring to Ireland as a burden is, well, rude. And suggesting that the fada doesn’t matter/everyone knows what you mean anyway (as I’ve seen people do when they make the same pivot from “Southern Ireland” to “Eire”) perhaps even ruder.
(Not drive-by sniping, my thoughts re: make-up already well-covered by others & no point in simply repeating them.)
[Attached image is a screenshot from an online Irish-English dictionary giving definition of Eire:
Similar words: Éire • deire • eile • eirg • eirre
eire, m. (gs. ~, pl. -rí). Load, burden. ~ droma, back-load. Tá sé ina ~ orm, it is a burden on me. Beidh sé d'~, ar ~, agat (é a dhéanamh), it will take you all your time (to do it). Tá ~ a dhroma d'hiacha air, he is weighed down with debt. (Var:f)]