Ajax was the strong and courageous Greek hero featured in Homer's "Iliad," known as Ajax the Great. But it's also the name of a foaming cleanser, and if you find that reference too strong, you might try the shortened Jax instead.
Ajax, Greek commander in Shakespeare's "Troilus and Cressida"
"Ajax suggests somebody who defies lightning and fools about with a spear. It's a silly name. A maiden aunt persuaded my mother to give it me. I think she mixed it up with Achilles; she admired the statue in HydePark." [WilliamLocke, "Septimus," 1909]
Ajax the Lesser, a Greek mythological hero. son of Oileus, the king of Locris. He was called the "lesser" , to distinguish him from Ajax the Great, son of Telamon.