My computers:
Dizzy-Guilty Gear X reference, named as such because of it's unusual triple headed configuration (3 different size monitors)
Miyu-Vampire Princess Miyu reference, small, cute, dark, and quite unusual. My MP3 player.
Yugo-Battle Angel Alita reference, not really all that important, but does more jobs than it should do. My router.
Ashram-Record of Lodoss War reference, powerful (well, it was when I originally built it), and gets the job done.
Dot-Animaniacs reference, small, unassuming. Used to be my router, now a backup.
I try and pick names from comics, games, or animated stuff that match the charactaristics of the system or how it's used. Though I'm too polite to name my work's computer Dan (MvC2 reference)