When Xenophon and the Ten Thousand Greeks (originally hired as mercenaries by Cyrus the Younger, who had been killed in an attempt to overthrow his brother and become king) traveled through that area (400 B.C.) the people living there were called Kardouchoi—thought to be the ancestors of the present-day Kurds.
What I find fascinating is that the areas in the map (where Kurds are in the majority?) constitute both oil-rich regions in Iraq AND the headwaters of both the Tigris and Euphrates.