Usually, Irish place names have just been adapted to English spelling, or translated. However, there are many that aren’t so obvious. Here are some examples:
Arklow – an tInbhear Mór, gen. an Inbhir Mhóir. This place-name is one of the relatively few occurrences of inbhear “river mouth” in Ireland (béal is more common). As everybody knows, Inver-this and Inver-that is typically Scottish, though.
Brookeborough – Achadh Lon. The Brooke family was granted the ownership of the village during the Ulster Plantations. Achadh Lon is what the place was called before. It means the same as Kosovo Polje, i.e. the field of blackbirds.
Carrick-on-Shannon – Cora Droma Rúisc. People often attempt to translate the English name back into Irish. as something like “an Charraig chois Sionann”. However, that is not the historical name of the place.
Dublin – Baile Átha Cliath (usually pronounced as “B’leá Cliath”), or in more literary language Áth Cliath (gen. Átha Cliath). The usual explanation is, that there were two towns to start with, Duibhlinn the harbour, and Baile Átha Cliath, which was the part further away from the sea. Thus, the English who came in from the sea called the place by the name of the old harbour, and the Irish-speakers who approached it from the interior called it Baile Átha Cliath.
Milltown Malbay – Sráid na Cathrach. This is a small place in Clare, near Spanishpoint (which is Rinn na Spáinneach in Irish, if you were curious). Milltown Malbay has been called Poll an Mhuilinn or Baile an Mhuilinn in Irish too.