the word 'fasces' does not exist in Italian.
From the Italian Treccani dictionary
fascismo s. m. [der. di fascio]. – Movimento politico italiano che trasse origine e nome dai Fasci di combattimento fondati nel 1919 da B. Mussolini
The word "fascism" does not exist in Italian either. We're using English and anglicised words.
The "Fasces" is a group of rods tied together with an axe, dating back to ancient Italian/Roman times, and comes from the Latin fascis ("bundle").
The word fascism no more derives from a political party (which simply pulled the word out of nowhere, did it?) than the words "democrat", "republican" or "communist" do.