Ancient mythology, while no longer a major religion, can still find references in nearly every household. Computer software, cleaning products, newspapers, and many other companies and products are named after mythological figures.
Ajax was the son of Telamon, king of Salamis. He was a great hero in the Trojan war, fighting for the Greeks. After Achilles, he was Greece's greatest hero. Indeed, it was Ajax who fought Hector in single combat after Achilles' initial departure from the fighting.
Ajax is a cleaning product manufactured by the Colgate-Palmolive Company. It comes in a powder with bleach for use on carpets and other household surfaces. It is also available as a dish detergent.
While no definite answer is given, the Colgate-Palmolive Company may have named the product Ajax because the mythological figure was a mighty warrior who "cleaned up" in battle. He needed no assistance from the gods, implying that Ajax cleanser is capable of cleaning up in the house without assistance from other products.