Tonatiuh Axe

Tonatiuh was the Aztec god of the sun. He was the fifth deity to hold this position, with the previous four suns each having died and ending a previous era of the cosmos in the process. It was thought that the job of being the sun was very strenuous, and that if he weakened, the sun would cease to move through the sky. Accordingly, the Aztecs offered human sacrifice to him. Tonatiuh was patron of warriors and lord of Tollan (heaven), which only dead warriors and women who died in childbirth could enter.

Prior to becoming god of the sun, Tonatiuh was a different god known as Nanahuatl, a weak and humble god of misfortunes. Two gods volunteered to sacrifice themselves by throwing themselves into fire to become the new sun: the weak Nanahuatl and the mighty Tecciztecatl out of duty and pride, respectively. Tecciztecatl hesitated to throw himself into the fire, however, so Nanahuatl did so instead. Nanahuatl became a weak yet haughty sun who demanded that the other gods sacrifice themselves to him. Tecciztecatl threw himself into the fire after Nanahuatl becoming a second sun, but the gods were angry with him and dimmed his face by striking it with a rabbit. So dimmed, he became the moon instead.

It is deeply unclear at this time why Square-Enix chose to give a weapon named after a sun god a function tied to the cycles of the moon.