There's definitely a middle ground there. My previous job used a format like, first two letters were the company initials, third character was a number pertaining to the office location, and the rest was typically a shortened description of the server. If there were multiple there would be a number at the end.

So, the servers were named like, ta2dc1 for a domain controller, which doesn't look like much to a layperson, but it made perfect sense to everyone in IT. As long as everyone follows the naming convention it will work.

At my new job all of the servers are named after comic book villains, and I have no clue what any of them are for, partly because it's not written down anywhere.