It is an anglicization of the Irish Ó Maoldúin, "descended from Maoldúin," which in turn was a legendary first name. This name means king or chieftain of the fort. According to the Annals of Loch Cé, they were said to be of royal birth and styled themselves as the Kings of Lurg, which is now in Co. Fermanagh.
According to The Surnames of Ireland by Edward MacLysaght, there are three distinct septs of Muldoon: Galway (around Uí Maine), Clare (whose names were generally Anglicised to Malone), and in Co. Fermanagh where the name is most common.
The family logo is Pro Fide Et Patria, Latin for "For Faith And Country."