My Irish side ended up as Callahan, but was definitely Callaghan before the Royal Navy lost the g, which the Irish do not regard as a different name than O'Callaghan, although they would write the latter in their records as O Callaghan, with a space, not an apostrophe. It doesn't end there of course, as the Irish gaelic is of course Ceallachain and of course O'Ceallachain is not regarded as a separate name. All these are just variants of the same name.

Traditionally all the above are descendants of Ceallachain, 10th century king of Munster, of the Eoganacht or Eugenian tribe, but so are McCarthys, Sullivans and some Kennedys (but not THOSE Kennedys, who are of the rival Dalcassian tribe or Dal gCas, and the Scottish Kennedys are another lot), because that king lived before surnames, and at least these three surnames were created later from various male lines, being originally the first names of his grandsons. Of course, all those names have variants of their own, in English and in Irish.

It is easy enough to trace this part of my family back to Ireland, and to Cork, where the clan lands were, although the original Ceallachain was from Cashel (Caisil) in Kerry, and I have no links going back anything like that far. The town in Cork that my family can be traced back to was only founded in 1725. We only have definite records back to 1852 in Ireland, and going forward from there to the present day in England, although we have 'suspects' in Cork in the 1700s via the Mormon records, and there are people in Pennysylvania that claim descent from them and who we have contacted.

That is actually my mother's fathers line, and the English side of my mother's family is pretty well known to us as well, thanks to her research. My father's family is more of a mystery. I suspect an Italian origin, possibly Jewish, but know almost nothing, and my cousin on that side is equally mystified. Sounds like a good case for yDNA testing. Of course, I came from England to the US myself, so that part is not exactly an unknown.