How do you name them?

For manned ships I usually use a hull designator prefix. DD, FF, CV

If you don't want to use Mk series you can use a M series where M1A3 would be the fourth update to of model 1. So if you do a huge overhaul and it is a new craft you call it M2 then the first revision would be M2A1. It works very well if you are not creative. A third version that is nothing like the models 1 or 2 can be model 3.

In general my naming scheme is very inconsistent.

Ships/Drones/Missiles: Some sort of fancy name alluding to their role, such as Laserstar or Mailman or Defense Drone. Relatively inconsistent.

Modules: Wherever possible, module names are slaved to their intended ship - so a Laserstar Corvette's main laser might be called Laserstar Laser 1GW, its radiators might be called Laserstar Laser Radiator, etc. to achieve nice, clean packaging of the designs. This minimizes module reuse, allowing me to fiddle with optimizing the module for the ship without horrifically breaking 10 000 other ships. Usually, if I want to reuse the module, I'll duplicate it for the something else to use. As much as modularity is fun, it and minmaxing a specific ship don't often go too well together.

xxx MK1,2,3,4...(e.g Laser Gunboat MK1 , Nuclear Missle MK2)

I usually have a short code to designate ship or weapon's purpose, followed by name followed by alpha-numerical variant designation. For names I usually try to come up with something a bit poetic and aloof. For example:

MCv Craddle of Fire - missile-centric ship
GS Raindrop - gunship
GS Towering Clouds - gunship
LC Everchanging Sky - drone carrier
LE Glint - small laser boat (I call all ships with laser as their main armament escorts)
HE Brilliant Dawn - 1 GW laser platform.

Capital Ships
Cross-section in four digits (eg. 0750) rounded to the nearest 10; this is so my own ships appear at the top of the list, and so ships that go into 1000+ continue to be ordered by increasing size, and the rounding is just because I'm an austistic spergburger. This is followed by the ship type. Older versions aren't retained so there are no marks. This goes like '0800 Frigate' or '1050 Carrier'. Ship type naming doesn't vary much since the ships don't vary much; I favour spreading systems around evenly. The progression goes Escort (~150), Corvette (~350), Frigate (~750), Drone/Missile/whatever Carrier (1000+). The Escort/Corvette/Frigate class names may be appended with single letters to differentiate different loadouts on the same chassis (Corvette N carries nuclear missiles, D carries drones instead, Frigate ND carries both), while all designs have an alternate version with droptanks where everything in the name is finally appended by T#, where # is the number of tanks, usually 4.

Full format example: 0750 Frigate ND T4

The roles implied by the names corvette and frigate are fairly ambiguous, unlike the history of the name of something like a '[torpedo boat] destroyer'. Of course 'escort' does imply a role, one to which they are actually quite restricted as they have to mooch delta-v off of larger ships to do more than orbital defence so it follows that they will escort them if they are with them at all. Corvettes are the smallest practical capitals and frigates are the most sturdy ships in a direct scrap, using their increased size to bear more armour without sacrificing delta-v, while bigger ships are increasingly given over to being queens that their little friends swarm around and defend like worker bees.

Missiles & Drones
Named for snakes and follow a stockalike convention (ie. Viper Nuclear Missile, like the Striker Nuclear Missile), though the exception is the Callisto, which is also designated as a rocket instead of a missile to emphasise its expendability or something. I think the name subconsciously derives from me imagining a massive constellation of these munitions exploding in patterns resembling the markings on Callisto's surface. There's no particular reasoning for the snake names, though missiles are long, thin and 'featureless' (ie. usually no radiators) like snakes. By contrast to this, drones are named after flowers and I actually give them five instead of my usual four or six radiators to look more like a flower from head-on. Personally I think flowers look quite scary, so hopefully it presents an intimidating visage to the enemy sensor personnel.

Modules
I shorten things like exhaust velocity and power ratings, so a 100.5 MW Thermoelectric Fission Reactor becomes a 100MW ThermoFission Reactor. This makes quick identification of modules in the limited space offered in the combat UI easier.

I usually go with letters and numbers, since it makes finding a specific ship easier. Two letters for the class's strong points, one number for the version, and two numbers for its dV.
For example, in the OS class of ships (made for Offense and Survivability), OS-257 is the 2nd design of the class, and has 5.7 km/s of dV.
Of course, you could make the two letters into an actual name for the class - OS-class could also stand for Overseer class.

I also had a naming system in the works a while ago, for a story I was planning.
Basically, ships come in two categories : Fleet ships (used in a fleet, so focusing on certain aspects), and Independent ships (used alone, so more overall capability over specific strengths).
So that gives you nice ship classes ! IO (Independent, Offence), IC (Independent, Carrier), FC (Fleet, Carrier), FE (Fleet, Escort), etc...

I just pick something tongue-in-cheek and put my "corporation" prefix on it