The Assassin organization is commonly called the Brotherhood in Assassin's Creed lore.
In Assassin's Creed Origins, Bayek and Aya establish the Hidden Ones in ancient Egypt as a secret order dedicated to protecting people from oppressive power. The organization is the predecessor of the later Assassin Brotherhood seen throughout the series.
The name changes over the course of the fictional history, so the answer depends on the wording. The Order of Ancients is the enemy organization in Origins, while Abstergo is a modern corporation linked to the Templars. In later eras, the Hidden Ones develop into the Assassin Brotherhood, which uses recognizable symbols, safehouses, and networks of allies.