My first real computer was a COMPAQ Presario CDS 633 (a 486SX/33 with 4 MB RAM). It ran MS-DOS 6.2/Windows 3.1 at first and later OS/2 Warp 3.
I first had to name it when I ran a news (NNTP/Usenet) server on it because OS/2 didn't have an offline news reader. I liked NewsReader/2 (nr2.exe) but I couldn't figure out why IBM believed that home users would be connected to the Internet all day. That was in 1994 and I was on (expensive) dial-up.
So I named it gopher.gopher.org. The name was only relevant for news articles anyway.
The name "Gopher" travelled from computer to computer until I had two computers in 1998. The last computer named "Gopher", a 1997 Pentium 200 running OS/2 Warp 4 is still in use by my dad for Microsoft Word 5.5 (which ran natively on OS/2!).
Starting then the slower computer would be "Cassidy" and the faster computer "Sundance". In 2001 my Power Mac G4/450x2 (dual processor) was Sundance and my UMAX S900 PowerPC 604e/233 was "Cassidy". And in the kitchen I had a server that was connected via cable going through a hole in the wall. It was named "Holeinthewall". The two clients connected to it I named the "Holeinthewall Gang".
I bought an iBook G3/600 which I named "Flyer". It is still with me, although the hard disk is broken.
In 2004, after I had moved to Ireland again, I bought an iMac G5 and named it "Hokem" (Hebrew for "wise man" and Yiddish for "wiseguy"). Two years later I bought an Intel Core 2 Duo iMac and named it "Xerxes" after the Iranian king.
And this year I finally added a new (white) Macbook named "Blacky".
I have three external hard disks: one 160 GB called "Databank", one 500 GB called "Opposition", and one that was made in Ireland (by Iomega); it is sort of metallic coloured and I use it for Apple's "Time Machine" backup application, I called it "DeLorean".
My HP PDA is named "Smallpox" (because it is is small, fits in my pocket, and is as useful as a disease).
My iPod Shuffle is named "Shuffeln".
And my iPhone, which was very difficult to register because of how iTunes works in Europe, is named "iCantbelieveit".