I saw this question asked over on the WALL•E Forum, and I just had to ask it here. I mean, what does going on an all-expenses cruise-liner vacation have to do with an axiom? 
According to Dictionary.com an axiom is:
Basically, what’s the connection?
I guess it basically describes the way of life after the space exodus: everything is taken for granted, being constantly waited on and sucked of all independent living is a way of life; a generally-understood, unspoken rule of living, if you will. It’s a universally accepted trend: a “don’t think for yourself, we’ll think for you!” sort of life. I guess that’s the only way I can see why they chose that word as a name for the ship.
little chef
Or maybe they just like the sound of it… 
BnL is your accepted truth, your logical way of life, and your epitome of happiness. BnL is your axiom so take a trip in our 1st class starliner, please enjoy your stay.
My take on it anyway. 
Hmm. I never really thought about why they named it Axiom. I just thought it was a cool name 
But the theory about BnL being an axiom does make sense.
“Axiom” to me sounds like an intimidating word, and a very Sci Fi-y time name. It just seems natural for a large and intimidating cruise ship in a Sci Fi movie.