"Ajax" was also a fictional name made up in 1937 by Disney as a joke on the Warner Bros fictional company "Acme"(Mostly known from Roadrunner), which was used in movies since the 1920s.
When watching either with subtitles in other countries they are sometimes translated from one to the other.
Acme is also of Greek god origin, and it was already being used before movies as a generic name to put companies on the first page of the alphabetically sorted telephone books or similar lists.
The soap brand owned by Colgate-Palmolive was named in 1947, so they were totally late for the Greek-god-generic-product-party.