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The name is derived from the Old Irish family name Ó' Madadháin which was anglicised most commonly as Madden or Madigan. It means 'little dog' in Old Irish. The modern Irish word for dog is 'madra' and little dog would be 'madra beag' or 'madraín' - not a million miles from the original. The name is probably most common in county Clare which is where my grandfather came from. I'm from Dublin and although there are not many Madigans in the city the name is well known because of its association with Public Houses - there are a number of pubs called 'Madigan's'.