The okasan of the okiya may adopt one of the geisha as her daughter (musume), to be her heir (atotori), therefore the girl lives in the okiya and all of the money she earns goes to the okiya.
The okasan of the okiya may adopt one of the geisha as her daughter to be her heir, or "atotori", if she does not have a daughter herself. Therefore the girl lives in the okiya and all of the money she earns goes to the okiya.