I'm guessing the word Axis came from the allied side describing their for.
Hiya, always room for more elaboration, but fyi you'll find some info on this here
What is a better name for the sides in WWI and WWII than "allies" and "axis" and "central powers" - /u/astrogator explains that "Axis" originated in a speech by Mussolini
What did the axis powers call the "allies"? - /u/jedimushroom introduces a few more terms, e.g. "Pact of Steel"
What did the Germans, Italians and Japanese call their alliance in WWII? /u/ParkSungJun supplies the term used in Japan "Japan-Germany-Italy Triple Alliance"