Wow, you have just found a great name for communist Ottomans. IOTL Şefik Hüsnü and Mustafa Suphi named communism as "iştirakiyyun"(communion/ism, participation/ism) in Ottoman Turkish. But I have to say Bedreddinism is a quite nice name. By the way Ottomans didn't use to names of Mesopotamia, Palestina and Syria much. I think Sham, Jarusalem/Jordan and Arabian Iraq(Irak-ı Arab in Ottoman Turkish) would be more fit.