Long time without biting... But the name is:

I stopped playing so-called memetic games a long time ago. But I liked this one - Thanks to Nicolás Valcarcel.
So, what are the current names?

Netbook

aikoa (temporary name, /methinks)

Laptop

malenkaya

Work desktop

mosca

Home server

cajita (yes, not very imaginative - it's a Mac Mini)

Main work server

lafa

Virtualization host

pulpo

Work firewall

joma

Other current machines have much less exciting names. Some of the older machines I have named (and with which I worked enough time to remember them) include shmate, lactop, conetontli, tepancuate, tlamantli... And many other long forgotten.
Oh, and... About a pattern? No, don't try to find it. Of course, if you do find it, I'd be delighted to know! :)