When I worked at NASA, I basically did both. We had fixed format official "cattle" names that included the organization code and the computer's inventory number. Those names were useless to humans, so I always also registered a human-friendly "pet" alias. It was a bit more trouble, but it generally worked well. The pet names also has some structure, with prefixes differentiating classes of systems (desktop, server, lab), but they were otherwise free-form and picked to be useful to the users.