Atreus was an ancient Greek King of Mycenae who bore two sons, Agamemnon and Menelaus. These two sons became kings in their own right, and were regarded as the "Atreides", meaning "sons of Atreus".
The Atreides name managed to be passed on throughout the ages, and along with it, its inherent nobility. This was evidenced by the fact that a noble House of the Imperium bore the Atreides name. Rulers of House Atreides were supposedly direct descendants of Agamemnon and Menelaus, the sons of Atreus.
Behind the Scenes
In the prequel books by Brian Herbert and Kevin J Anderson, a curious story is related whereby the Atreides name is handed down by Agamemnon the Cymek, not Agamemnon the son of Atreus, as alluded to by Leto Atreides II in God Emperor of Dune (novel).