Eire is the official name of the RoI in Gaelic and is the form of the country's name used on the stamps, coinage and passports. It is interchangeable.

It may have connotations of a united Ireland but until v. recently, the state of RoI/Eire claimed sovereignity over the whole island of Ireland which is why I, a Co. Antrim born child of two Scots parents can claim Irish as well as British citizenship.