I've been look at some other players' posted save games and I was surprised to see standard planet names and non descript ship names. For a massive game, I don't know how people keep track of the dozens if not hundreds of ships and planets if you don't rename them.
For planets, I usually group them by location. Then rename them by purpose and planet type. So an example could be 'a Nestor II R rad'. The 'a' refers to the group of stars at a certain location. The 'R' means it's a research specialized planet. The 'rad' means it's a radioactive. I'll name by planet type if I haven't had the chance to research the extreme colonization techs yet. If I'm looking at the civilization manager, I can immediately tell how I want to use this planet. I can also sort by name and see how I distributed specializations within a given cluster of planets.
For ships, I first give them a name, then list the important numbers. So an example could be 'Axe (10g 5b 4 20)'. This is a combat ship with 10 gun strength, 5 beam defense, 4 movement and 20 hit points. Race, resource and other bonuses will change the actual numbers, but at least the ship name will instantly tell me the relative strength.