Here is my ship's naming chart:
XYz1-[a name of my choice] IaM1
Let me explain:
XY is for the race's name design, as said before in this thread, in order to avoid naming conflict between different races similar ships.
z is the global class of the ship. Atm I only use 4 letters:
t for transport class ships (ie colony, constructors, miners, troop transports, and any unarmed "civilian" ship, ect...)
e for exploration ships (ie scout, survey, but also fleet support ships)
a for attack ships. By attack ships, i mean those with at least one engine (and weaps)
d for defensive ships. By defence ships, I mean those without engine, since I only use them for star/planets defence (even if I usually use them as "first strike defence" strategy

)
So that way, in planet shipyard, I quickly see where is wich ship when plenty ship design already exist. Just have to remember the needed ship's [a name of my choice] design name, and even if I forget it, I'll quickly find it again.
The number (here 1) is for hull class size. 1->5 Tiny->Huge, 6-> Cargo, since it will help getting each ship type be displayed also by hull size category, helps a bit to spare time

The [name of my choice] is obviously without the [ and ], and different for each ships.

Ia is a roman numeral followed by an alphabetical order letter. It is here for differents versions of the same ship, the leap between I to II to III is usually when I switch engine tech and the letter beyond is when new weaps, miniaturizing, ect, comes in.
M1 is not alway used. It means Mod 1, then M2 for Mod 2, ect. I use this when playing another game when I set a different path for techs using same ship design, since I saw that there was a flaw in the roman numeral followed by alphabetical letter naming chart, creating a new updated ship who was, let's say, between IIb and IIc. So that new ship got named **** IIbM1, ect. So no more trouble, no more naming conflict.
I don't bother naming ship with speed, attack, defense, and other stats in their name, I use the description of the ship for this. I tried to do so, but I found that ship names got really weird (especially military ones with different kinds of weaps and defenses) and painful to remember.
I'm french, so I don't really use "classic American ship naming chart" (such as DD, BB, BS, CVN, ect...) but instead a "classic French ship naming chart" of my creation (almost similar to american one, but in french)

PM me if you want to know it.
So the description, in example, for an attack cruiser class ship would looks like something like this (english translated here):
CC v G-M/S-AM. (Large)
A Colony ship would be (french here):
VCl v rapide LP. (Cargo)
Obviously, CC is the ship type, I usualy says that tiny hulls are "fighters", Small hulls destroyers, med hulls cruisers, large hull battleships and huge hulls dreadgnaughts. VCl here means "Vaisseau CoLon" (colony ship), "rapide" means "fast", LP for "Longue Portée" (Long Range).
v comes here for "Version"
G-M means Guns-Missiles (no number behind the letter since a quick look over the ship stats is ok, it would be redundant to rewrite those numbers, and I like small desc easy to read), if the ship would use beam, i would use the B letter. The separator between weaps and def is /.
S-AM means Shields-AntiMissiles, A for armor if used.
Then the size of the hull for a quick glance since it is not truly visible in the interface in planet shipyard.
Since my military ships comes in two major versions, "attackers" and "defending" ships, I dont bother with speed naming chart since "attacker" means no more that there is 2 engines on board, and defending not at all. If needed, i will add "slowest", "slow", "fast", "fastest" for civilian designs with just zero, one engine, or more than 2 engines, ect, assuming that having 2 engines is "normal" speed, and no need to write it in the desc... Fastest means that the design is fully fitted with engines, and just the generic "civilian" module onboard.
I also don't put any range extender on my military ships, assuming the next war will be on my own civ borders, since I'm not really a "warmonger" (until I got really cool heavy sized capitals ships with plenty hi-tech weaps on board), but if needed I would design a special long range striker.
So in description (especially for "civilian" ships), SR will come for Short Range, LR for Long Range, VLR for Very Long Range, at my appreciation (translated in english here, using french in my game, as said before). The "default range" here is usually having just one or two range extender on board.
I also write in desc for those cheapest colony ships or constructors that they ARE actually the cheapest ship of a given hull size.
One last word, I have to say that it was this thread who made me create this relatively simple naming chart, before that, I was naming my ship in a pretty anarchic way, with only a (nice) name of my choice for a new designed ship, and only one letter in alphabetical order behind for different version types, like i was used to do in MoO and other older 4X space games, such as Pax Imperia, first of the name

...
Needless to say, ship building is a waaaaaaaaaaay easier with a good naming chart, it makes you spent a little more time at the beginning but saves you a lot of time in the long term for those hardcore gamer (still get a real life, yes, thanks you for concern

) we are!
Edit: Added a number for hull size in the generic name of the ship.