What is the name of the Assassin's Creed faction founded by Bayek and Aya?

The Assassin's Creed faction founded by Bayek and Aya is the Hidden Ones.

Bayek and Aya establish the Hidden Ones in Assassin's Creed Origins after confronting the Order of the Ancients, a secret organization seeking political control in Ptolemaic Egypt. The new group adopts principles of secrecy, service, and resistance to oppressive power. Its members operate from hidden bases and assist people affected by the Order's influence.

The Hidden Ones are the historical precursor to the later Assassin Brotherhood. Origins therefore functions as an origin story for the series' central organization, showing how a personal struggle develops into a durable network. Aya, who takes the name Amunet, becomes especially important to the Hidden Ones' early development and connection to Rome.

The Order of the Ancients is the principal opposing faction in Origins and is the ancestor of the later Templar Order, not the group founded by Bayek and Aya. The Levantine Brotherhood belongs to the era and tradition associated with Altaïr, making it another tempting but incorrect answer.