[PvK]

The AI never re-names any ships.

The ship picture changes during a refit, unfortunately. I've been disappointed by that since SE3.

Another thing you can do, if you don't mind losing some flexibility, is to put a gifted ship into a fleet whose strategy is set to NOT break formation. This way the fleet strategy will override the ship strategy, so you won't have to worry about the gifting nation giving your ships a lame strategy (at least, not until damage forces the ship to break formation, in which case some of the design strategy might be used, but formation is broken mainly when the ship loses its weapons IIRC).