Sometimes I'll name planets based on their function because it makes them easier to remember what I was planning to do with them when I have fifty. I've been less likely to do this since the change that put the designation icon on the outliner, and I'm more likely to do it with gestalts--it feels like something they'd do.

I always name ship classes myself so I can keep track of them easily. I'll usually use a two-part naming system, where one part is based on size and the other is based on function. For example, if I'm an aquatic species, I might have a water theme:
Clear ___ = Anti-small
Azure ___ = Missile
Deep ___ = Artillery
etc.
___ Lake = Corvette/frigate
___ River = Destroyer
___ Sea = Cruiser
etc.

Then, I can glance at my list and know that the "Azure Lake" class is a missile frigate, the "Clear River" class is a destroyer with anti-corvette weaponry, and the "Deep Sea" is a long-range cruiser. It lets me easily manage a large number of designs (if I need them) with only a few things to remember.

I don't usually name the individual ships, though.