I've heard that the Jewish name "Cohen" comes from "Khan" as well. Nope.
Go read the Bible.
Kohanim were a priestly caste. These were the descenants of Aaron, the first High Priest. There have been Y-chromosome studies of self-proclaimed Cohens from Africa to Europe and India to Morrocco and America showing that most share the same male ancestor.
Now, it is possible that some Eastern European Jews with names like Kagan, Kaghan, or Kahn, have another root.
Some Ashkenazi Jews (although genetic data shows a small number) are desceneded from
Khazars. In 740 CE, the Khagan Bek (the military/political leader of the Khazar Empire {khagan=Khan or Khans}) converted to Judaism along with a number of Khazar nobles.