God of War director Cory Barlog confirmed the name of Kratos’ son through twitter. According to the discovery that Fabiano Banin made in the introduction music of E3 God of War that was shared yesterday, the name of Kratos’ son Atreus.
— Cory Barlog (@corybarlog) January 13, 2017
When Atreus is looking for the name, it turns out that it belongs to Greek mythology. “Atreus is the granddaughter of Tantalos, son of Zeus, son of Pelops and Hippodameia, brother of Thyestes and Nikippe.” (Wikipedia)