People (in the UK at least) often distinguish between the republic, the island and Northern Ireland by prefixing with "Republic of". So I don't really understand what your point is because nowhere in the article does it claim the official name of the Republic of Ireland is the Republic of Ireland. By your logic every time someone wrote an article referencing "the UK", it would be appropriate to reply "do you mean the United Kingdom of Great Britain and Northern Ireland, because that's its actual name!"