Giving it just a tiny bit of thought it's very obvious to me what "Ax Ishmael" means.

It means:

"I am a crazy bastard who is about to go on a shooting spree, and since I am a crazy bastard I need to make up a cool name for myself which I will use when I send pictures to a mass-media outlet, and since I just made this cool new handle up on the spot and no one knows it's me, I'll need to write it on my arm in ink so they'll be able to tell it was me."

It's very simple.

The Meaning of 'Ax Ishmael'