Not cool, a lot of Ashkenazi Jews aren’t Zionists and not live in Israel.
Name itself is coming from legendary figure of Ashkenaz, grandson of Japhet who as the direct descendant of Noah symbolise Germany. Germany was called Eretz Ashkenaz in Yiddish since medieval, and so Ashkenazi Jews = Jews in Germany, from where they spread to nearly entire west, north and east Europe when they were running away from pogroms.