According to some of our best and most widely-published authorities on Irish surnames (MacLysaght and de Bhulbh), “O hUallaigh” has come from the Irish word “uallach”, with a meaning such as “proud” “vain” or “boastful! This gives us names such as Holy, Holey, Holley, Hooley, Hooly, Howley, Wholly, Whooley, Whooly. Don’t worry unduly about the spelling as the English-language versions are, for the most parts, just approximations of the original Irish-language names which tried to capture the sound of the original Irish word. The names listed above are found mostly in West Cork, where ‘O hUallaigh’ seems to have originated. The name Holy and Holey (often interchangeable spellings) are largely confined to North Cork, around Castlemagner and Mallow with the Whooley version being very common in West Cork.
Shane writes that “The Irish for Holly (the tree) is Cuileann, which is the connection to the original surname Ó Cuileannáin”. Shane is correct. The names “Cullinan” (found mostly in Counties Clare-Limerick, Wexford-Waterford-Kilkenny) and “Cullinane” (found mostly in County Cork but also in Waterford-Wexford-Kilkenny) come from this root. The surname ‘Holly’, found mostly in Kerry-Clare comes from Mac Cuilinn but in County Antrim there is a family of Welsh origin, McQuillan, which then got to be mistranslated as “Holley” on the assumption that it was originally an Irish name!
During the great wave of Irish Emigration in the 19th Century, many of our emigrants could not read or write (even their names). Many were Irish speakers, some with little English. Consequently, when they met Emigration Officers, Census takers and other Officials, they were not in a position to insist on a particular spelling of the name. So, as you approach old records, do not expect consistency of spelling!
If this is not complicated enough already, I will offer one last complication. There is an English surname, ‘Holy” (originating in Britain) with no connection to the Irish surnames discussed above.
So if your name is any one of those above, you actually need to have some details about your roots before you know how to write it in Irish!