Below are several versions of the origin of the name. While it is generally considered a "Milesian" name the second source near the bottom claims it is a branch of the Tuatha Danaan. Commonly translated as "Devotee of St. Challan" this is apparently wrong. See the explanation below.
The following was collected by the late Dr. Frank Milhollan (1923-1992), who was a professor, and it was shared by one of his friends who had accesss to his genealogical materials. It is an excerpt from the Ulster Journal of Archealogy, Ser. 3, Vol. 1, 1938, pp. 115-117.
The Origin of the Surname 'Mulholland' by Margaret E. Dobbs The family of the above name are known in Irish records as the Ui Mail Challainn, the official guardians of the precious relic, St. Patrick's Bell. The first holder of this office of whom anything is known was Cathalan U Mael Challainn, named as "Maer in chluic" ("Steward of the Bell"), in the inscription on the shrine made for the bell between 1091 and 1104. The last holder of office died at Edendubhcarrick (Shane's Castle in O.S., 1835) circa 1800-1820. There is no record as to when the office was created, and no pedigree of the family is known to exist. A clue, however, has come to light as to the possible founder of the family in Ulster. There were other Ui Mail Challainn in County Limerick in 1012, and in County Westmeath, but they may be eliminated from consideration as having no connection with the North. Now, all Irish surnames are formed from the Christian name of some ancestor. Who was the Mael Callainn whose descendants took his name? The name itself is an unusual one. There were many compounds of Mael (tonsured; devotee of), and some like Mael Duin, Mael Sechlainn, Mael Coba, are of frequent occurrence. Mael Callainn literally means "devotee of the calends—the first day of the month." Similar forms are Mael Domnaig — "devotee of Sunday," and Mael Chorgais — "devotee of Lent." All these are very rare. For instance, the index of one MS. alone (Rawl. B502, Bodleian Libary) has over 5,500 personal names all dating before 1200. Mael Callainn occurs twice. The Senchus Sil Ir (Antrim and Down genealogies before 1100) has over 2,000 names. Mael Callainn occurs once. The Four Masters have the name twice, the Annals of Ulster once. It was therefore a very uncommon name, which makes identification more possible.
The use of surnames developed in the ninth century. The first instances in the Annals of Ulster occur in 855, 858, 866, 871, etc. They increase in number from that onward. The O'Neills of Tyrone adopted their surname after 920. It first appears in the annals in 943. They took the name in honour of Niall Glundub (ob. 919), the gallant defender of Ireland against the Norse. The surname U Mael Challainn appears in 1012, and again before 1090. It must have been taken from an ancestor before those dates, and after 850. Now, the leading races in Northern Ireland in early times were known collectively as the Ui Neill, who, as time went on, split into Ui Neill, Ui Domnaill, Ui Lochlainn. The royal family were known as the kings of Ailech. This was the district in South Inishowen round Grianan Ailigh (Greenan Mountain), their stronghold and assembly-hill. In 797 Aedh Oirdnidhe, King of Ailech became High-king. He died in 819 (A.U.). He had five sons:—
"Niall Faille (recte Caille), Mael Duin from whom descend the Ui Mail Duin in Uib Echdach, Fogartach from whom descends Cinaed Ua Mail Ograi in Fininne, Blathmac from whom descend the Ui Duibenaich, Mael Falann (recte Calann) who held Dun Druing in Inishowen."—(Facs. Rawl. B 502, p. 14a, 23.) "Niall Kaille, King of Ireland, Mael Duin . . . Fogartach . . . Blathmac . . . Mael Falland who has the district of Dun Druing in Inishowen."—(Laud 610 See Zeitschrift für celtische Philologie, VIII (1911-2), p. 292.) "Niall . . . Mael Duin . . . Fogartach . . . Blathmac . . . Mael Falland who has the district in Dun Druing in Inishowen."—(H. 2. 7. P.4a, T.C.D.) ". . . Mael Callund who has the district of Dun Droighin in Inishowen."—(23. D. 17., p. 41, R.I. Acad.) "Six sons of Aedh Oirdnidhe: Niall Caille, Maol Dun, Diarmuid, Fogartach, Blathmac, Maol Callann."—(Leabhar Clainne Aodh Buidhe, P. 21) "Niall Caille, Mael Duin, Diarmait, Cionath, Fogartach Fuilbocc, Mael Culland."—(McFirbis Genealogies, P. 126.) The variations in spelling do not affect the identity of the names.
Aedh Oirdnidhe died in 819. Niall Caille was born in 789, and died in 844 (A.F.M.) or 845 (A.U.). Mael Duin died in 865. Mael Callainn may therefore be dated between 800 and 860. His grandchildren in the tenth century, when surnames came into general use, would very naturally take the name of the ancestor who linked them with the royal house of Ailech. There are, moreover, some clues in the family history which seem to connect this Mael Calainn with St. Patrick. His father, Aedh Oirdnidhe, seems to have had a special devotion to the saint. As King of Ailech it would seem the natural thing for him to have honoured St. Columba, his kinsman. This was not the case.
In 804 (A.F.M.) Aedh exempted the clergy from military service at the prayer of the Primate of Armagh and his clergy. The question was judged by Fothad na Canuine.
In 805 he proclaimed the observance of the Law of Patrick (A.U.).
In 808 he severely punished the Ulaidh for profaning the shrine of Patrick (A.U.).
In 816 the community of Columba went all the way to Tara to denounce him (A.U.). No reason is given, but he was evidently no patron of Derry. His son Niall Caille, had got his confessor appointed archbishop of Armagh in 825 (A.F.M.). A nephew, lord of the Airghialla, expelled him, and Niall without hesitation fought his nephew and reinstated his nominee. This archbishop would have had good reason to favour the family of such supporters. Possibly the appointment of the Ui Mail Challainn dates from this period. There can, unfortunately, be no certainty on this point. All that can be claimed is that the rarity of the name, the dates of Mael Calainn and his family, their connection with Armagh, their habitat in Ulster, all combine to suggest that this son of Aedh Oirdnidhe as the ancestor of the Ui Mail Challainnn who were the "Keepers of the Bell."
Admitting this possibility, it is a matter of interest to identify the district of Dun Druing (Droighin) in Inishowen. This is surely the same as Td. Dundrean, in the parish of Burt, Inishowen West, north of the railway at Bridge End. It is northeast of Greenan Mountain, and not far from Eskaheen, where the first kings of Ailech were buried. There is one fort-circle marked on O.S., sheet 47, which may be the remains of the dun which gave its name to this land. Judging from later references, the Ui Neill and their dependants gave up Inishowen to the Ui Dochartaigh of Fanad, and moved south to the rich lands of Derry, Tyrone, and the shores of Lough Neagh. This occurred sometime before the Norman invasion, as in 1197 the Ui Dochartaigh fought the invaders of Inishowen (A.F.M.). It is therefore likely that the Ui Mail Challainn had gone south before that date with their suzerains, the Ui Neill. They were in Loughinsholin barony by 1400. Though we have no details about Mael Callainn's descendants, the following facts are recorded about his relations. The wife of Aedh Oirdnidhe, and the mother of Niall Caille, was Meadb, daughter of a Connaught prince. Whether she was the mother of all the sons is not stated. There was a sister, Land, married to the King of Airghialla. It was her son who quarrelled with Niall Caille about the primacy of Armagh (see Revue celtique, XLVIII (1931), p. 186). Niall Caille died a hero's death, trying to save a man from drowning. His son, Aedh Findliath, a man of energy and ability, was High-king from 861 to 879. He was consistently victorious in fighting the Norse invaders. Their chief stronghold in Ulster was on Lough Foyle, which was unpleasantly near Dun Druing. Mael Callainn must have been thankful when his nephew destroyed it in 864. When Niall Caille was High-king, his brother Mael Duin was called Lord of Ailech. His descendants did not stay there, as they are located in Uib Echdach (Iveagh), County Down. Two of his daughters, Dirbail and Indearb, are given in the Ban-shenchus (Revue celtique, XLVII (1931), p. 187). Mael Duin died in holy orders, a pious custom for aged folk in those days. His descendants took their family name from him, U Mail Duin (Muldoon).
Blathmac's descendants, on the contrary, were called the Ui Duibenaigh, so must have adopted a surname at a later date. Their pedigree has survived in 23.D.17, p. 41 (R.I.A.). Nothing is known of them or their habitat.
To conclude—that the MSS. quoted above do not mention any descendants of Mael Callainn need not imply that he left no family. The destruction of MSS. by the Norse, and the disorganization of records by the Norman invasion, are quite sufficient to account for all omissions of this sort. Between 832 and 943 Armagh alone was ravaged by invaders seven times. Sixteen outbreaks of fire are recorded between 840 and 1196, due to different causes. Bangor, Moville, Derry—all suffered equally; hence many gaps in the surviving family records.
Delbna Geoffrey Keating describes seven areas referred to as Delbna, that is Dealbhna Mhor, Dealbhna Bheag, Dealbhna Eathra, Dealbhna Iarthair Mhidhe, Dealbhna Shithe Neannta, Dealbhna Chuile Fabhair, and Dealbhna Thire da Loch in Connaught. At least four regions in southern Uí Neill territory are denoted as Delbna. Around the 12th century these included: Mac Cochlain (Mac Coughlan) of Delbna bEthra (Garrycastle, Co. Offaly), Ua Finnallain (O'Finnallan, Fenelon) of Delbna Mor (Delvin barony, Westmeath), Ua Scolaidhe (O'Scully) of Delbna Iathair (Delvin and Rathconrath baronies, Westmeath),
Ua Maoil Challan (Mulholland) in Delbna Bec (Fore barony, co. Westmeath). '
In addition, Delbna regions were noted in the province of Connacht, one of those cited as Delbna of the Two Lakes (Dealbhna Thire da Loch) near the River Shannon. Reference to this is under (see Connaught).
6. Delbhna Bheag, or Delbhna Bec, were based in what is now Demifore in Co, Westmeath. Their chiefs took the surname Ua Maoilchallan, or Mulholland.
O'hEochadha of great showers, Over high Cinel Aenghusa;33 Over Dealhbna Beg,34 brave his children, Is O'Maelcallann, the fair and hardy.