Anyone else noticing that when you research a new armor or drive system you get the better stats but the name of the system or armor does reflect the change?

Unfortunately it will take me awhile to test to make sure, but I don't remember encountering this problem awhile back when I did my play throughs.

I think it only happens with custom races. Pre-made races seem fine.

New armor upgrades have to be refit on to a ship; new drive bonusses occur immediately (or as soon as a ship arrives in-system, if it's in transit). The name should be reflected on the drive, but not the armor (if the ship isn't refit).

Hmmm ... I generally use a custom race, but I am going off of memory and I haven't tested again myself yet paying attention to the problem.

Ship drives are upgraded instantly. Ship armor needs a refit. This is intended mechanics and is exactly what you're seeing.