when I name my ships, I write them down (mostly) so that I don't double up on names. I usually don't name Infantry, since there are so many of them, but sometimes I name them '1st Berlin Garrison', or '1st Dresden Garrison' for example.
It also comes in useful for keeping track of how many kills the ships made, for example, in my current game the highest scoring ship is CA (Armored Cruiser) Scharnhorst, which was built in Stuttgart in AD 800 during a war, the Scharnhorst has so far sunk 7 enemy ships.
Oh yeah, the designations that I use are:
TR: Trireme (my added unit)
GL: Galley
GS: Galleass (added)
CR: Caravel
SP: Sloop (added)
FR: Frigate
GA: Galleon
PR: Privateer
SL: Ship-of-The-Line (added)
IC: Ironclad
DD: Destroyer
CL: Light Cruiser (added)
CS: Cargo Ship (added)
CA: Armored Cruiser (Heavy Cruiser)
BB: Battleship
BP: Pocket Battleship (added)
CV: Aircraft Carrier (Carrier)
SS: Submarine
SN: Nuclear Submarine
CVL: Light Aircraft Carrier (added)
CM: AEGIS Cruiser