From The Oxford Names Companion
Halliday in English and Scots; from Old English haligdaeg holy day, religious festival. The reasons why this word should have become a surname are not clear, perhaps it was used as a nickname for persons born at Christmas or Easter.'
From Burkes Commoners
'With the settlement of this people on the borders of the two kingdoms, began the harassing and petty warfare which may be said to have continued until long after the Union; and tradition affirms, that 'a holyday' became the warcry or slogan of the chief and people of Annandale, whenever they made a 'raide' or foray upon the Saxon border - for they accounted every day HOLY, that was spent in ravaging the ememy's country.'
The wars that in the aftertimes so fiercely raged between two neighbouring and rival nations, thus arose from the hatred that existed and long continued to exist between two distinct people,the Saxon and the Gaul, the oppressor and the oppressed. The Clan, when provisions became scarce were summoned to make a holyday, and in proof of the probability of this origin of the name, the eminence where the 'Annandale Moss Troopers,' were accustomed to assemble when a foray into England was ordered, still retains the designation of the Halliday Hill. (OS Landranger Series sheet 85 NY091741) Whether the derivation be correct or not, there are now no means of ascertaining - but the evidence is complete, that the chieftain, who first assumed the surname, had his castle or strong tower, near the source of the River Annan, and about two or three miles above the present flourishing village of Moffat, so celebrated for its mineral waters; at the Corehead the ruins of this castle may still be traced, and there we may suppose that generation after generation had lived in Celtic greatness as chiefs, and had hunted the wolf and the wild boar in the woody vale, when more profitable pursuit of Saxon beeves was not necessary or advisable.
It was also suggested by researcher Clarence Halliday (1963) that the name might have more ancient roots. Roman invaders called the people of Annandale 'allodil', which might have translated from Latin as 'those who cultivate their own land'. The idea being that when the Roman legions penetrated the valley of Annan they were struck by the fact that the peoples there, a mixed race of peoples, lived on lands owned by themselves. That is, no feudal type system existed as the Romans were accustomed, but one more like a freehold tenure. The medieval Latin word 'allodiālis' is apparently the root for Allodial land title. The similarity of this Latin word to the Old English surname could indicate a corruption of the old word with the new meaning. Evidence for this interpretation is however admittedly thin.
Lots of variations including Holyday and Holliday.