In science and mathematics, an Axiom is a premise that is accepted as fact.
In Pixar's WALL-E, the Axiom was the name of one of the luxury cruise ships where humans lived after the Earth became uninhabitable.
There is a computer algebra system called Axiom.
Axiom does not appear in the Social Security Administration's name database. I think it would fit in well with other trendy names that contain the letter 'x'.