Short answers, pulled from the story.
F.T. Brooks published a book titled Neo Theosophy Exposed in 1914 to label the new direction of the movement. This work formed the second part of an earlier volume called The Theosophical Society and its Esoteric Bogeydom.
The faction led by Olcott and Besant remains headquartered in India under the name Theosophical Society - Adyar. Annie Besant and Charles Webster Leadbeater introduced clairvoyance as a primary method for exploring past lives and the astral plane within this group.
William Quan Judge ended his association with Henry Steel Olcott and Annie Besant during 1895 following a dispute over forged letters from the Mahatmas. He took most of the Society's American Section with him to form a separate organization before dying in New York City about one year later.
Alice Bailey herself introduced the term New Age to describe this broader spiritual shift. Her work alongside figures like Dion Fortune and Aleister Crowley eventually shaped Anton LaVey's Satanism and L. Ron Hubbard's Scientology.
Margaret Thomas published Theosophy Versus Neo-Theosophy around 1924 to provide a detailed critical comparison of the two systems. Critics argued that the movement had strayed too far from its foundational texts after Annie Besant and Charles Webster Leadbeater integrated Catholic rituals through the creation of the Liberal Catholic Church.