The secret society opposed to the Assassins in Assassin's Creed is the Templars.
The series presents the conflict as an ancient struggle between the Assassins, who value free will, and the Templars, who seek peace through control and order. Their rivalry spans historical periods and is repeatedly reframed through different characters, institutions, and political movements.
The fictional Templars draw inspiration from the medieval Knights Templar but are not identical to the historical order. In the games, the modern Templar organization operates through Abstergo Industries, which publicly presents itself as a multinational company.
The Hidden Ones are an early form of the Assassins, while the Medjay are Egyptian protectors associated with Bayek. Abstergo is the modern corporation linked to the Templars. These names are connected to the same universe but are not alternate names for the Templars themselves.