Our network doesn't have a real name. (I'm sure it calls itself something, but that's the name it and other computers call it...) There's no real scheme to our naming, except that the computers that I have often name themselves, either cleverly or based on personality traits of the boxes themselves.
My laptop is named Tigereye, because she is a Dell. (A little too much Jennifer Roberson, back in 2000, I think...)
sorcha007's computer is named Sorcha. She named it. The two former computers of hers were Red and Enki.
marxdarx's computer is named Acknar. He named it.
The computer that was originally merely called "the new computer" named himself Neo after a while. He is happiest running Linux. He is an ancient Compaq.
Neo has a clone/twin who was originally going to have several different OSes. Then we found out his hard drive was damaged. His name is Lord Mark, as he is a clone with brain damage/multiple personalities. He will probably, once he gets a new HD, evolve into a squat, fat, deadly box with an attitude -- or several.
My former palmtop, a Visor Neo, was named Inanna; she was twin to a palmtop named Ishtar. I was planning on naming my next Visor Neo, if anything, Trinity, but I never got another one. I now have a Palm Vx named AzureBlue, for the color of her case. This is, clearly, a literary joke as well as a play on my own name. (Yes, I answer to my online name more than I do my birth name...)
The Mac Quadra 660 AV that I took over for a few years back in the late '90s was named Majel, because she could speak in a very pleasant, if flat, female voice, and respond to voice commands. (swallowtayle and I programmed her to respond snarkily to a few voice commands: if we said, "Computer, open Monopoly," she would respond, "This module is not programmed for game-playing.")
And of course the old computer I was on for a week back at my parents' house -- his name is Guardian. You know, because the Guardian of Forever said, "Let me be your Gateway"....
[Edit: next time I have a box with a really big