If you are talking about a class of ships, I name them by their characteristics:
2 Plasma 10 PC
Colonize 7PC w 2 Life
Troop 13 PC
At the end, I start naming everything starting with "A" or "AA" so they show
up at the top of list. I don't have to scroll when I keep pumping out troop
ships.

Interstellar Cruiser, Medium destroyer, escort-F1, battleship... all traditionnal name

I like my Imperial BattleShip who look like starwars one

I have a whole list written out. Depends on the hull class, and the weapon base (that is, the weapon type I use most on the ship):

Tiny:
Beam: B-Class Javelin
Mass Driver: D-Class Javelin (D is for Mass Driver)
Missle: M-Class Javelin

Small:
Beam: B-Class Cavalry
Mass Driver: D-Class Cavalry
Missle: M-Class Cavalry

Medium:
Beam: B-Class General
Mass Driver: D-Class General
Missle: Chupacabra (carries ONLY missles, nothing else, except for a small engine. Makes for a powerful attacker in a fleet.)

Large:
Beam/Mass Driver: Star Commander (usually only one of these in a fleet)
Missle: Cerebrus (Like the chupacabra, it only carries missles, along with a small engine. Deadly in a fleet, but lousy in the field.)

Huge:
Any: Star Admiral (Certain doom.)

Perhaps I'm a bit ... um, detail oriented ... but I have a system I use. I name my ships by the hull size, the race I'm playing, some short unique name, and the ship's individual characteristics.

For example, a common name is SH Mage 4x6x2x23, where:

S = small hull (T, S, M, L, H are the options)
H = human race (I play all races and save all my designs)
Mage = short, unique name
4 = ship speed
6 = attack rating; might be followed by b, m, or g for beam, missile, or gun
2 = defense rating; might be followed by s, p, or a for shield, point defense, or armor
23 = range of 2.3 parsecs

This makes it so I can easily determine the characteristics of each ship at a glance. It also makes upgrading easier by letting me find old ships quickly. Finally, when I go to build a new ship, the ships are listed in order of decreasing size from huge to tiny. This works because the letters designating hull size work out to be in alphabetical order. So, the biggest and most powerful ships are always at the top of the ship selection, which I find very helpful. Anyway, this little system works for me.

mini fightas (initial 3 beam, small hull ones- relatively slow and no range enhancements)
currently made a vamp- huge hull, with all the modifications (two fully upgraded military resource bases) 97 beam power, 28 movement. (four hyper warps mark iii)
Hive- (advanced troop transport which can transport around 8k -14k troops) - huge hull, one disruptor 3, two hyperwarps (mark iii) and jammed with adv troop modules.
death bunny- my missile cruiser

dart- high move, missile attack.

dragon frieghter- (yes i dont bother with trade till a LOT later) cargo hull, two range enhancers, rest engines.

there are others... but i forgot

I like to give them fancy names.
Tiny Hull Fighter Thorn
Small Hull fighter Shellfish
Medium Hog
Large Focus on weapon Archangel
focus on armor Dark Knight

I also have a medium hull with a lot of sensors called illuminati
and some ohter ship i cant remember

I've created a list of names from ancient greco-roman mythology and roman emperor names (from wikipedia). When I crerate a new ship, I go down the list and add a prefix indicating the type, class and power of the ship. For example:
'LS-05 Minotaur' is a Small hull doing5 damage points with it's Laser.
'GM-10 Augustus' is a Medium hull Gunship doing 10 points of damage.
'CR-05 Heracles' is a construction ship and so forth..
Obviously, smaller ships dont get deities names, but names of creatures or mortals.

I will probably add names from egyptian and norsk mythologies soon.

I usually pick a name that suits my chosen race, and then change the 'Mark' number for every upgrade.

For instance, my custom race, the Shinra Electric Power Company from Final Fantasy, has a lot of ships that are named in a 'businesslike' fashion. I then put some time and effort into the descriptions.

I change the description for each upgrade as well, just to be complete.

Wow, I really like some of these above ideas.

Here's how I do it now

I usually have designated ship classes as by size and main weapon type such as

TF (Tiny Fighter) TFM or TFB or TFD (Missile Beam mass Driver) and small name such as TFM Knat I
DE (Initial Small Escort ) DEM or DEB or DED and animal name such as DEM Bear II
FG (Later Small Frigate) FGM or FGB or FGD and a class name like a large bird FGM Eagle IV
CA (Medium Hull Cruiser) CAM or CAB or CAD and some fancy name dependent on the game CAM Olympia III
BB (Large Hull Battleship) BBM BBB BBD and names of cities,states, stars etc.
BC (Large Hull Fast Battle Cruiser) BCM BCB BCD cities states stars
DN (Huge Dreadnaught Class) DN named after stars of gods or dark things DN Hellraiser III

When I upgrade my fleet designs when I get a major new weapon or before a new invasion, I upgrade the design and add a Roman numeral behind it.

I may start individually naming ships Large hulls or Huge Hulls. I name fleets as my Main Battle (best atk fleet) task forces (TF Alpha) or all my fast transports as (INV 1) invasion 1 etc.

I usually add the atk and def strength and speed in the comments line below the ship name ( M40 P40 sp 9)

So a complete ship name might be

BBM Omega III
M40 P40 Sp9

which would be a large hull battleship with base missile atk factor 40, Point defense 40 Speed 9, that was the 2nd generation of that design ( I may have gotten better missiles and upgraded the design and then upgraded the design when I got better engines)

I may have renamed a individual ship as BBM Adventure which the game would show up as a BBM Omega III class vessel.

I use lists of stars, roman and greek gods, battles, historic navy ships, battles, generals, animals, insects, states, cities etc. I just google to find a bunch of lists and have them pasted into a word file. I try stay consistent game to game.

I usually referance various Science Fictions, fantasies and other genres, as well as some from our own history. I take the star trek convention of naming the first ship of a class by its class name. Also, I'll have some kind of acronym before each ships name depending on what kind of race I'm playing. Here's a few from my favourite game

Galaxy Class: A referance to the Star Trek TNG class, it was my first ever ship. Name of indivdual ships include
RSF(Republic Star Fleet) Galaxy,RSF Terran Way,RSF No Compromise

Stonewall Class: A heavy frigate, so named as it was primarily a defence based ship.
RSF Stonewall, RSF Terran Dawn, RSF Drath

Defiance Class: My first ever big anti-ship vessel. You could call it a referance to the Defiant of DS9, but it wasn't what was on my mind at the time
RSF Defiance, RSF Alliance, RSF Vengance, RSF No Retreat, RSF Benden, RSF Claymore, RSF August Star,
RSF Spartan

Battlestar class: My first huge hulled ship, eventually becoming the mainstay of my fleet. No prizes for guessing where the name came from.
(I switched to United Federation Fleet when I changed government) Most of these are named after my planets, with a few exceptions.
UFF Earth, UFF Benden-B, UFF Solesia, UFF Terra Nova, UFF Galactica, UFF Midway, UFF Caeser, UFF Agememnon, UFF Defender, UFF Achilles, UFF Titan

Guardian: My strongest class, so named as I'd just come into ownership of a lot of planets and they needed defending.
UFF Guardian, UFF Iconia, UFF Persia, UFF Federate Star

Call me crazy, but I name ships what they are, and just read the stats to determine role. I never use 'spam defences', and throughout a game I will probably only use four or five different designs, and simply update them with new weapons and engines and retain the original name. Makes it hard to determine what version 'cyber warship' something is... but that only happens when you're low on cash.

I use a class letter (P = patrol, F = fighter, OD = orbital defender, D = destroyer, C = Cruiser, B = battleship). I used to name each class (e.g. P-1 Gnat, P-2 Blackfly; F-1 Hawk, F-2 Falcon, D-1 my wife and kids' names, etc.). Having done that for a while, now I am more "practical" and use the name to give the ship's specs, e.g.:
F-3 2-0-0 0-1-0 would be a fighter (small hull) with a speed of 3, beam attack of 2, and missle defense of 1. This is helpful for easily grouping ships of the same speed in fleets, and seeing a ship's attack & defense at a glance.