The common definition of the O'Dalaigh surname today is, "deriving from
Dalach meaning 'one who is present at assemblies'; the root word is Dail, now the official title of the parliament of the Republic of Ireland". A connection is also possible to the long tradition of scholarship and poetic achievement associated with those who bear it, since the ollamh of Gaelic Ireland had a place of honor at the tribal dail as a man of learning and a poet.
Other evidence points to an even older more significant meaning, based on the claim by the pagan Irish that they were offspring of their gods. This evidence is found on several Ogham stones which contain the oldest known form of Irish writing.
An example from the Gowran Stone;
DALLO MAQA MUCORI MAQI ERACIAS MAQI LI
and one from the Dunbell Stone of Kilkenny
BRANITTOS MAQI DECARI DDALLOS
These inscriptions appear to invoke either pagan gods or mythological figures with names similar to the ancestral "Dalach". A third ogham, Monataggert II further specifies
the Dalach (Dalagni) as sons of the eponymous ancestor (Dali). In many cases the mythological ancestor was female.
DALAG N I MAQ I DALI
From this evidence and other data associated with times of antiquity in Ireland, it would appear that there are reasonable grounds for assuming the family name "O'Dalaigh" has a godly or mythological significance.Indeed, it provides a more logical probable meaning of the name O'Dalaigh than the more popular versions built almost entirely on definitions given in modern dictionaries for supposed parts of the family name.
From "History of the O'Daly's, The Story of the Ancient Irish Sept, The Race of
Dalach of Corca Adaimh" by Edmund Emmett O'Daly (Chicago, 1932).