In Assassin's Creed Origins, the secret organization that predates the Assassins is called the Hidden Ones.
Bayek of Siwa and Aya establish the Hidden Ones near the end of the game's story. Their organization grows out of the Medjay's campaign against the Order of the Ancients, a powerful secret society manipulating political leaders in ancient Egypt.
The Hidden Ones protect people from abuses of power while operating covertly. Their principles, methods, and hidden bases provide the foundation for the later Assassin Brotherhood. The series therefore presents Origins as an origin story for the organization rather than as a tale of an already fully developed medieval Brotherhood.
The Order of the Ancients is the main opposing organization in Origins, and it later evolves into the Templar Order. Calling it the Assassins would be historically incorrect within the series' fictional chronology: that name and institution emerge later from the Hidden Ones.