Inspired by the late Chris Harbison, and as an attempt to flesh out sparse data from the 18th century, I used Bill Macafee's data from the 1766 Religiou Census of the baronies of Loughinsholin and Keenaght (basically East Co. Londonderry, minus the barony of Coleraine) to ascertain if some given names were predominantly Protestant or predominantly Catholic. Caveats: these data are transcriptions of transcriptions, the originals having been lost in the 1922 Four Courts fire in Dublin. I've made obvious substitutions, mostly expanding abbreviations. (John from Jno., William from Wm., etc.) I've combined variant spellings (e.g. Brian, Bryan), and expanded obvious familiar versions (Daniel from Dan). I've tried to be careful with all of these; since, for example, I don't know if Ar is Arthur or Archibald, I haven't used it. There were a total of 3424 entries on the census, of which 68.5% were Protestant (I haven't broken down Protestant into Established Church and Dissenter, though that would be possible). I used any name that occurred 6 or more times, which accounted for 2965 of the 3424 names. Only three names were female, because the census counted heads of household, and because many of the women were simply listed as 'widow'. Here are the results.
The red line gives the percentage one would expect if there were no religious bias in naming. There is a clear break around that point, indicating that indeed some names were predominantly Protestant or Catholic. Those that are very heavily Catholic include clear transliterations of Irish (Gaelic) names: -- Phelomy, Brian, Owen, Shane and Cormac. Names that are not obviously associated with saints, either Old Testament (Benjamin, Samuel, Adam) or secular (Alexander) are heavily Protestant. But many differences are inexplicable (why is Matthew Protestant and Paul Catholic?).
Also a little surprising is the absence of influence of politics. Approximately 75 years after the Williamite war, William and James are almost equally favored by Protestants. My parents used to claim Catholics did not take the names of English kings, but that's obviously false (Edward, Charles, Henry, Richard). My suspicion is that this is because names were simply passed down through families, somewhat like hereditary diseases. My own family heavily used William, Henry, John, James and Thomas. Perhaps this really reflects some early conversion from Protetantism.
And finally, Patrick is intriguing. It is of course of Irish origin, but more recently than this census the Church of Ireland embraced St. Patrick. However, at the time of the census it was clearly not much used by Protestants.