Although the American way of pronouncing "Mahoney" sounds strange to us in Ireland, I'm thinking it may well have come directly from the Gaelic. There was a huge wave of emigration from Ireland in the mid 19th century (famine time) and many/most of the emigrants would have been native Irish speakers. I'm not sure what Gaelic surname is associated with Mahoney or O' Mahoney, but MacMahon is equated with Mac Mathúna. In Munster Irish, the stress is on the middle syllable of "Mathúna", and it sounds closer to the way the Americans say Mahoney than the way the way the Irish do.

Next we should demonstrate that "Baloney" is an Irish word ... and did you hear the one about the politician Dukakis being not of Greek origin, but Irish; his immigrant forebearer a Dubh-Chathasaigh from Gréig na Manach?

and - seriously - another spin-off from the Pogues was a band called the Popes