Irish: "brown/dark" (i.e. "dun", such as the Dun Cow), or possibly "noble"
In the Lebor Gabala Erenn, Donn son of Míl son of Bile is one of the seven sons of Míl who set out to conquer Ireland. He was jealous of his brother Ír for rowing faster towards Ireland than anyone else, and he uttered a curse upon Ír, which caused his oar to break and Ír to die. For this, Donn (here called Éber Donn) was judged by his brother Amorgen as unworthy of any part of Ireland. Though he was supposed to never set foot in Ireland, we later find that he insults Ériu, the goddess of Ireland, when at a conference at Uisnech.
After this insult, Amorgen is able to persuade Ériu to support the Milesian invasion; Amorgen and Donn lead their men back to their ships; spells send them beyond the ninth wave, out of the borders of Ireland. Donn seeks retaliation, but is drown at the island now Bull Rock, but formerly Tech Duinn--"the house of Donn."
This Tech Duinn is, according to the Dindsenchus, the place where "his folk shall come to" when they die; "and for this cause, according to the heathen, the souls of sinners visit Tech Duinn before they go to hell, and give their blessing, ere they go, to the soul of Donn" (Gwynn, IV, 311).
As his other name: Éber. It is also associated with another brother Éber who battles yet another brother, Érimón, over the kingship of Ireland. The island was divided in half, the north to Érimón, the south to Éber, whose land stretches "from Ath Cliath to Tech nDuinn" (Dillon). The numerous Ébers which appear in Lebor Gabála, and their constant losing to other brothers may point to the Indo-European twin-sacrifice: specifically, the Éber figure is sacrificed by the Érimón figure in order to create the kingdom. Similar figures are Romulus and Remus, and Yama and Manu, both of whose myths feature the sacrifice of a brother in order to create order. The alternative is that Amorgin and Donn are the twin-sacrifice figures, with Amorgin allowing Donn to be killed by the Tuatha Dé Danann in order to win Ireland.
At any rate, Donn does seem to be associated with an island of the dead, and may have originally been a figure similar to Caesar's Dis Pater, god of the underworld from which the Gauls claimed descent.
Dillon, Myles Lebor na gCert: The Book of Rights. Dublin: Irish Texts Society, 1962.
Gwynn, Edward. The Metrical Dinshenchas, v. IV. Dublin Institute for Advanced Studies Dublin (1991 first published 1906; reprinted 1941). URL: http://www.ucc.ie/celt/published/T106500D/index.html.
Macalister, R.A.S.Lebor Gabála Érenn: Book of the Taking of Ireland Part 1-5. Dublin: Irish Texts Society, 1941.
Rees, Alwin and Brinley. Celtic Heritage. New York, Grove Press, 1961.