Something I didn't really mention before, is my affinity for individually naming the destroyer class and up. For me, it goes:
Tiny = Fight
Small = Heavy (two-man) Fighter or Corvette
Medium = Frigate
Large = Destroyer
Huge = Heavy Cruiser

Every Large class or Huge class ship I build, I have to give a custom name to. Often I name the Huge ships design "Flagship MK '#'", so I don't really have to think of a name there. I usually go for a name dependent on my alignment
Evil - Dictator, Tyrant, Enforcer, Nemesis, etc.
Neutral - Defender, Protector, Guardian
Good - Sword of Light, Spear of the dawn, Arrow of Destiny (Yes, kinda preachy, but I like playing the 'good crusaders').

I do try to theme my names, though. Sometimes I go for an Nordic theme (Mjolnir, Thor, Loki, Valkyre, etc), sometimes an Avian theme (Sparrow, Hawk, Falcon, Eagle, etc), recently I'm trying a Mammal theme (Wolverine, Grizzly, Panther, Cougar, etc).

Link
Interesting bit of history there:

• Corvettes were small single-gun boats that were eventually replaced by the larger Frigates
• Destroyers (about the same size as Frigates) got their name shortened from TorpedoBoat Destroyers, and eventually took over the torpedo boat's job.
• Cruisers were so named because they were the first vessels to be capable of long range independent operations, whereas Destroyers required tenders.
• Battleships came and eventually went, being replaced by Carrier groups with destroyer escourt.

But then, space may be a different can o' worms...

In an effort to never have to design another ship after playing through the game three times I have almost unique name for every level of Tech in any combination. No space for any creative naming though

Minitiarization Level
Primary Weapon Type
Primary Weapon Grade (Highest)
Role
Defence XXX [sap] (Highest, s - shield, a - armour, p - point) 000 = "" (blank)
Propulsion (Highest)
Extras (Sx - Sensors, Lx - Life Support) (x - Highest Level)

Role
Constructor
Colony
Troop
Scout = No Guns, Small Frame
Sensor = No Guns, Medium Frame
Def = Defender - No Engines, Tiny Frame
Bull = Defender - No Engines, Small Frame
Int = Interceptor - > 40% Engines - Medium Frame
Gun = GunShip - < 40% Engines - Medium Frame

eg

10 Contsructor I3
10 Laser3 Def
40 Phasor5 Int 050W2

Never needed to build greater than medium ships...

but but at peace ... not gives a good drubbing like a Woden class Battle ship. espically fun for taking out those pesky military bases.

Duh

Recently i've been giving them birds names, raven, hawk, etc. Some other names too like Raptor. Before I used names like Raider, Devastator, Avenger, etc.

I wont be doing anything like naming ships so I "never have to design another", I have all my appearances down so i just, before i beat the game, clear all the tech things from the ships i design so i keep the appearance. I then, every so often, just upgrade everything and keep how it looks. When I get the new hull i have a blank hull ready to use.

The reason i dont do it the way the guy said above is because i, on occasion, upgrade all my ships of that type and you cant do that unless you give it the same name.

From the list of WWII US Navy hull designations posted by liveload, here's a few that made sense for the ship missions that I commonly build:

AGF (Auxiliary General Flagship) - Flagship
AGS (Auxiliary Geographical Survey) >> ASC (Auxiliary Stellar Cartography) - Scout ship
ARS (Auxiliary Repair, Salvage) - Salvage ship, for anomalies
YP (Yard Patrol craft "Yippies") - defenders
PF (Patrol Frigate) - small-hull anti-insurgency
PE (Patrol Escourt) - tiny-hull fighter wings
PY (Patrol Yacht) - converted yacht, for those purchased scouts
XAK (Cargo/Merchant Marine) - freighters
LCI (Landing Craft, Infantry) - troop transport
DD (Destroyer) - medium-hull combat vessel
CL (Light Cruiser) - early large-hull or late medium-hull combat vessel
CA (Cruiser) - large-hull combat vessel [rarely used]
BC (Battle Cruiser) - late model large-hull or early huge-hull [haven't built one]
BB (Battleship) - huge-hull war ship [haven't built one]

B/c the ship lists in drop downs and the shipyard is alphabetized, I slap a prefix before all my ship names so I know what they do, then label them (usually)

By size and ratings. S7-B12A10 = Small hull, Speed 7, Beam 12, Armor 10.

Scout 5-7 = Sensor 5, Speed 7

Transport 3-12 = 3000 Troop capacity, Speed 7.

Not very original, but very organized (for me anyway).

I name my ships by their role (i.e. size, speed, offensive/defensive nature) and then use letters for minor upgrades and Roman numerals for major upgrades. So ex. I start out with small, slow ships that are only meant to give me some defense:

Sentry, Sentry b, Sentry c, Sentry II, Sentry IIb

Then I build a Medium-sized defensive ship that I don't give much engines 'cause it's also meant to stay at home:

Sentinel, Sentinel b, Sentinel II

Other ship names I use:

Corsair -- for a fast medium sized ship
Frigate / Corvette -- normal medium sized ship
Destroyer / Dreadnaught -- normal large sized ship
Battleship / Star Destroyer -- huge sized ship

I think of the Star Wars universe in my naming, hence a Dreadnaught is smaller than a Battleship.

Utility ships I name like:

Fast Transport
Long Range Freighter
Freighter II -- long range and fast freighter

AngleWyrm:

I created a "new" hull designation yesterday.

ADN or Auxiliary Dreadnought. Hehe let me explain. I tried a different tack for the early game this time around and chose to ramp up diplomacy techs. I built a spin control center on my homeworld when I reached total majesty. By that time, the rest of the galaxy were making plans on how to divide up my territory. As per suggestions on the forum, I took a couple of weeks to get some basic weapons and defense. I then packed a freighter full of weapons, armor, engines, and a little life support. They could hit as hard or harder than any current capital ship, and outwardly appeared to be well defended. "Pocket Battleship" didn't quite work for a hull designation, despite the obvious connotations in how they were used. One good shot from a real warship and the subterfuge would be lost, but the AI seemed content to leave them alone. The Auxiliary Dreadnought bought me enough time to get my naval build-up well underway before actual hostilities commenced.

Hehe, just thought I'd mention it.

JohnBigBootay: love your name, Monkeyboy!

I name mine after Caldari ships from a game called Eve Online.

liveload:
Stealth technology at it's best

Recently I've been naming combat vessels for their primary armament, with their name being the letter of the weapon.
Laser ships:
PE Lucinda-401, a laser patrol escourt
PF Lazerous-405, a laser patrol frigate
DD Lucifer-405, a laser destroyer

The numbers just let me know how fast/far they can go, so I can fleet them appropriately

I just think of cool names and class them like.
Fireclaw Fighter
Empire Battleship
Knight Cruiser
Halo Cruiser
Royal Battleship
Omega Dreadnought

any else discover that you can rename enemy fleets and ships.

I usally give them designations such as

Fleet Born to die

Festering Wound and such.

Duh

I name them after their personalities =D

Moxy: Tiny angular hull with forked wing attachments, no armor to give room for the 3 railguns. Must always be the first to attack or will fail miserably..

Curmudgeon: Heavily armored large hull, sporting two claw-like arms bent forward from underneath holding 2 plasma weapons in each "hand", and a 5th on its head. Reasonably fast but not much range.

Dumpling: Huge angular hull with very few structural additions, missiles everywhere and 2 phasors. Slow but good range, some armor.

Grendel: Huge long hammerhead-type hull, engines separated from body(a-la Enterprise), with two towering structures in the back holding 3 phasors each, sprinkled with photon torpedos along the bottom. Good range and speed, decent armoring and countermeasures.