Is Paul Atreides Descended From Agamemnon?

Yes. In Frank Herbert's books, House Atreides traces its line back to the House of Atreus in ancient Greece, the royal family of King Agamemnon. Paul's son Leto II, who can reach the memories of every ancestor, says he has followed his father's line all the way back to that house. So Paul Atreides is descended from Agamemnon's family, many thousands of years down the line. (God Emperor of Dune; Children of Dune)

The name#

In Greek myth, Atreus was a king whose sons Agamemnon and Menelaus were known as the Atreides, the sons of Atreus. Agamemnon led the Greeks against Troy, and his family's story is among the bloodiest in Greek tragedy. In Aeschylus's Oresteia, Agamemnon comes home from Troy and is murdered by his wife Clytemnestra, who blames him for sacrificing their daughter, and their son Orestes kills her in turn. (Oresteia)

Herbert's Duke Leto, Paul and the rest of the family carry that name many thousands of years later, as a Great House of the Landsraad. Dune itself doesn't stop to explain it. The later books do. (Dune; God Emperor of Dune)

What Frank Herbert's books say#

The first direct statements come in Children of Dune. Alia, drowning in the voices of her ancestors, hears one of them announce itself as Agamemnon, her ancestor, and demand to be heard. Later in the novel one of Paul's twins, speaking to Irulan, whom they call the childless wife of their father, says the Atreides go back to Agamemnon, know what is in their blood, and have a bloody history they are not finished with. (Children of Dune)

God Emperor of Dune is plainer still. In his journals, Leto II says his paternal grandfather was The Atreides, a descendant of the House of Atreus who traced his ancestry directly back to the Greek original. Elsewhere Leto says that, through his father's line, he has gone right back to the House of Atreus in his inner memory. Since Leto can live his ancestors' lives from the inside, that is about as close to proof as the books get. (God Emperor of Dune)

What Herbert never does is name the generations in between. There is no line of descent from Agamemnon to Duke Leto in the six novels. The Atreides family tree shows how little is filled in before Paul's grandfather. (God Emperor of Dune)

The other Agamemnon#

The prequels by Brian Herbert and Kevin J. Anderson add a different figure with the same name. In Dune: The Butlerian Jihad, a man born Andrew Skouros traces his family back to the ancient king, takes the name Agamemnon, and becomes the leader of the Titans, tyrants who later had their brains put into machine bodies. (Expanded books: Dune: The Butlerian Jihad)

This Agamemnon fathers Vorian Atreides, who turns against him, joins the Butlerian Jihad against the thinking machines, and finally kills him, throwing his brain canister from a window. The expanded books make Vorian an ancestor of the later Atreides. None of this comes from Frank Herbert. (Expanded books: Dune: The Butlerian Jihad; Dune: The Battle of Corrin)

So the expanded books give two answers in one: Paul descends from the cymek Agamemnon, who himself claimed descent from the Greek king. If you only follow Frank Herbert's novels, there is just the House of Atreus. (Expanded books: Dune: The Butlerian Jihad; God Emperor of Dune)

Why it matters#

Our reading, and it is only a reading, is that Herbert chose the name for what it carries. The House of Atreus is the classic story of a family cursed to kill its own, and the Atreides books keep returning to it: Paul fights a jihad he can't stop, Alia is possessed by the grandfather she killed, and Leto II rules as a tyrant for thousands of years. The line in Children of Dune about a bloody history that isn't finished is the books saying so openly. (Children of Dune; God Emperor of Dune)

Paul's ancestry has another side too. His mother Lady Jessica is the daughter of Baron Harkonnen, which is covered in why is Paul Atreides a Harkonnen. (Dune)