What's yours called?
My current WIP is going to remain faithful to the original. It's a Hang-on cab.
I have other designs in a portfolio. One theme I'm trying to create is a pink Bubble Bobble version to try and entice my GF to allow a small cab in the living room. I'm not really very artistic, but I can tap into some artistic talents in some of my groups if I needed to.
I'm keeping names to myself until I can actually start the projects. No sense in giving other people ideas when I want to use them first

It took me awhile to come up with mine too (Arcadia 2007) -- but there's some family history behind it--see my "Inspiration" page on my cab's site: http://www.freewebs.com/vidmouse/inspiration.htm
I think tying in a little of who you are helps.
You remind me a little bit of what's happening in my family. Except I lived in a technologically dry well. I doubt there was anyone who understood circuit theory within 30 miles of where I lived.
A single cabinet is called an "ARCADE MACHINE". Being that MAME emulates many arcade machines, it is fitting to call a MAME cabinet an "ARCADE" as it contains many different "Arcade Machines" all in one package.
So there!
Out in the wild, I don't think I've ever heard anyone refer to a particular cabinet as an, "arcade machine." Although I have heard people refer to them as, "arcade games." The word, "arcade," tends to carry the connotation of a room comprised of many gaming machines. Interestingly, if you look up the definition of, "arcade," the primary definition is not related to gaming machines at all, rather the structure of the room itself. That would explain why places like Fresh Choice refer to seperate areas of the restaurant as, "arcades." Go figure.
In any case, I would avoid naming a single cabinet with arcade unless it was
specifically part of the name.
That's just me, I'm not out to offend anybody. It just stuns me when people put so much work and effort into their cabinet only to ahem... name it something chintzy like MAME or Arcade whatever. People can name their machines whatever the hell they feel like really. It's the games inside that count.