I think Mussolini commonly went by "il duce", while dux seems to be going back all the way to ancient Roman times, where it's a noun related to the verb for "to lead", meaning leader, essentially. It and its root gave us "duke", "duct", "produce", among many others.
"Duce" derived precisely from dux, and a famous fascist motto was "dux mea lux". If any italian finds this repo, it would be impossible for them not to think of Mussolini, I assure you.