Searching for my ancestor James O'Brien, possibly from Cultrasna, Kiltimagh District, possibly son of John O'Brien and sister to Anne or Anna O'Brien

The Irish given name Tadhg (pronounced like "taig" - with the "ai" rhyming with the English word "tie") was anglicized over the years in various ways, mostly as Thaddeus, Timothy, and (less often) Thomas, but also with forms like Tigue.  Thady is a shortened form of Thaddeus which one often sees in 19th century parish registers.  It was a not uncommon name in the Kiltimagh area. It was the name of one of my great-great-grandfathers who lived just a few townlands away from Cuiltrasna (which is the modern anglicized form of the townland name), and in various old records his name was anglicized as Thaddeus, Thady, Timothy, and Thomas, though he would have remained Tadhg to his Irish-speaking family (Irish was still regularly spoken at home in that area until the early 20th century).  Tadhg is not a particularly popular name now, perhaps because it is used as an insult against Catholics by Protestants in Ulster (as in: "He's a Taig").  I have some distant Judge and O'Brien relatives in the area, by the way, but don't know the exact connections.

In case you're interested, you can see more about Cuiltrasna at this link:

https://www.townlands.ie/mayo/gallen/killedan/kiltamagh/cuiltrasna/

In Irish, Cuiltrasna is Coill Trasna. The word "coill" means "woods". The word "trasna" usually means "across", but it can also have the meaning of "wide" in some contexts, so Coill Trasna presumably means "wide woods". The word "coill" is a common component in place names in the area, so the area was probably much more forested in the past than it is now (although reforestation is now taking place in many areas). The main local town, Kiltimagh (older spelling Kiltamagh) is Coillte Mach in Irish. The meaning of the name is disputed, with “milking woods” now believed to be most likely, with less likely meanings being “outer woods” or “woods of the plain”, based on the Irish form Coillte Amach, which modern scholars believe was not the original Irish name. The local parish church is the Church of the Holy Family in Kiltimagh, but the Catholic parish name is Killedan, from the Irish Cill Liadáin (“Liadán’s church”).