Actually I used to name them after girls (I just do that now for my guitars), but recently I started naming my main system builds as SHODAN inspired by System Shock lol my laptop and netbook or M-SHODAN and M-SHODAN II respectively (M for Mini =p )
I named my NAS Skynet for some reason...
What would you name you system? You never mentioned your idea hehehe
Anyways, being an English nerd, I have a long list of words I love. I usually just pick one of those, or jump around a thesaurus until I find one that has the right feeling.
My computer is called NeoGeo just like the system. I think I was probably the only kid in the late 90s who still played on this system. All my friends had SNES's, N64s, Playstations and Sega Saturns/Genesis. Still had fun times with this system playing King of Fighters '94.