Okay, so from what I understand, during the Armenian Genocide the Ottoman Empire, convinced its christian subjects had the potential to become a fifth column, decided to kill every christian in the empire. While this did include Armenians, it also included Greeks, Assyrians, and many others. Why then, is the genocide named after the Armenians? Wouldn't "The Christian Genocide" be a better term?
I am not sure where you got the idea that the Ottoman Empire decided to kill every Christian in the empire. This is not true. The Armenians were specifically targeted because they were thought to have been collaborating with the Russians over eastern Anatolia, not because Christians as a group were a fifth column. In response, they were forced on a death march into the Syrian desert. Greeks in Ionia and Istanbul were generally left alone until after the war, when both Greece and Turkey engaged in a sort of ethnic cleansing via population transfers over the Aegean (however, this is not genocide).
There is a lot of good material on the meaning of genocide and its role in World War I, especially towards the Armenians, but I think you misunderstand Ottoman goals during World War I.
Moses, A. Dirk, ed. Empire, Colony, Genocide.
Quataert, Donald. The Ottoman Empire, 1700-1922.
Reynolds, Michael A. Shattering Empires: The Clash and Collapse of the Ottoman and Russian Empires 1908-1918.
Rodogno, Davide. Against Massacre: Humanitarian Interventions in the Ottoman Empire, 1815-1914.