Origin of the Star Trek Naming Convention
mturner: The name of the machine was a function of what the lastest trek movie/series that was out. Prior to ST:TNG coming out, machines had the names of TOS and movies (Kahn and Saavik were from "The Wrath of Kahn"). This was not always the case, but could give you an idea as to when something came out.
Picard and Yar were two from the ST:TNG days.
Dax was from the days of of DS9. The name 'Dax' won out over others because 'cisco' would have confused the lab staff (thats not a router!). 'Odo' and 'Bashir' were other possible names. Dax won out because it was a hot and sexy machine... William wanted 'Bashir' for the same reason. 'Wormhole' was the gatorbox that appeared during the DS9 timeframe.
After DS9 this wasn't held as strictly, but machines occasionaly were named in sets or relating to the age of the system (scotty being an old 3b1 - captian, I can't boot any faster, it will take me at least an hour).
Vger (after my time) was named as such because it was the biggest machine (and fastest) in the trek series.