Something interesting I found while looking up this specific title for Izou: according to this twitter user, Okada Izou wasn't called a Hitokiri (Manslayer) until after the Bakumatsu. Instead, people called him Tenchuu Jouzu na Izou-san, meaning "Good-at-[delivering]-divine-punishment Izou-san". Hence, some took to referring to FGO's Izou by this name too. Whether this story is true or not doesn't seem to matter.