The form "Éire" is widely used nowadays in Ireland to refer to the country "Ireland". However, in colloquial speech, the form "Éirinn" (Dative Singular to be exact)is used instead of "Éire". That this usage has a long history is evinced by its use (granted misspelt)by Irishmen and Irish-Americans in the eighteenth and nineteenth centuries.
We don't get hung up about this in Ireland so why lose any sweat over it abroad?
Annraoi