Imagine that some mystery virus has taken down or infected several boxes on your network and management want to know exactly what has gone on. In this scenario things are pretty sober and you really don't want to have anyone asking why the computers are named after some characters from a TV show or pretentious Greek myth characters. They won't see the funny side of it (if there is a funny side).
It is therefore much better to have important network machines and kit named in a logical manner, e.g. location-purpose-number.
As for what people have on their own desks, some people might detest whatever your cutesy name scheme is and be irked at having to use a machine called 'jigglypuff' just because they really never liked Teenage Mutant Ninja Turtles. They might also not really take to their workstation being impersonal, e.g. 'ldn-gfx-23'. Hence, on the desktop let people have a machine name of their choosing.
It is therefore much better to have important network machines and kit named in a logical manner, e.g. location-purpose-number.
As for what people have on their own desks, some people might detest whatever your cutesy name scheme is and be irked at having to use a machine called 'jigglypuff' just because they really never liked Teenage Mutant Ninja Turtles. They might also not really take to their workstation being impersonal, e.g. 'ldn-gfx-23'. Hence, on the desktop let people have a machine name of their choosing.