Within my circle of wheelin buddies, every rig each of us have built over the years has managed to earn itself a nickname. Once it has earned a name, sometimes it is broadcast to the world with a sticker along the top of the windshield.
That being said, often we do not come up with the nickname of our rigs ourselves, it is more likely to be chosen by someone else within the group based upon experiences building the damn thing, or experiences on the trail.
Some examples are:
Dodgey -- A full-size '80's Dodge built with Chevy drivetrain (sitting on 44's)
Shakes -- Another full-size 80's Dodge diesel that had a tenacious childhood (sitting on 40's)
Fire Chief -- An '98 XJ, red in colour (didn't see that one coming, did ya?), that was previously a fire marshal's work vehicle, had all sorts of holes drilled in the interior/exterior for their CB and radio equipment etc.
Swamp Donkey -- '88 Toyota 4Runner, custom built to the point of non-recognition, renowned for being ugly but damn can it ever crawl through anything you throw at it
Lost Limey -- '98 green XJ, owned by a limey bastard, who actually 'lost' the damn thing on the trail. Got left behind by the group on a night run after getting stuck, had to abandon it on the trail, find his own way back to camp, and when the search party started, couldn't find it until 4pm the next day.
These are just a few examples, but like I say these are rig names that have been earned appropriately, and chosen by others. Works really well if you ask me