I always named my ship The Brook's Cane, mostly to see who else gets it.

But I love naming my crew after various people I know, it makes for great discussion telling someone how they died in an engine fire

I can't believe i'm the only one who called my crew after Starfox series :D

My ship is obviously called "Great Fox", and i have Fox, Falco and Peppy.

I don't mess with the crew (except breaking up an occasional sausagefest in case of a fully human crew) but I captained these:

Red-Tail (duh) - my first win, after which I started naming ships
Clarity - red-tail on normal
Eternity - Engi 1, for the exploit which I ended up not using
Lotus - Engi 2
Arete - Stealth 1
Zephyrean - Stealth 2
Avenger - feds
Viper - mantis 1
Awesomesauce - mantis 2

Having got bored with a lack of further unlocks, I am now taking a break from the game. The first crystal I get to fly will be named Lollipop.

Finally beat the game a few days ago with the Krasniy Oktyabr.

It had the cloaking device ?

I believe so, but not from the outset; was using the standard Kestrel ship.

I always name my ship The Heart of Gold.

Oh smeg, the Cat! I always fly with Kochanski as navigator ;-)

Highest rank with the Engi Cruiser is currently 'Ten Ton Tabitha'.

Rock b is 'Heavy Metal' with Angus, Ozzy, Lemmy, and Lars.

Zoltan b is 'The Radiance' with Gamma, X, and Infrared.

Crystal b is 'The Bad Habit' with Meth, Crack, and Bath Salts.

Engi a is 'Doughnut of Doom' with 01, 10, and Wild Bill on guns.

Fed cruiser is 'The Penetrator', piloted by Ron Jeremy (other crew members' names change).

In the few games I've played this far, I've always gone with the default Kestrel.
For the next game, though, I'm planning on naming it either Heart of Gold or Normandy.

On a related note, I wonder if Kestrel will once be a name which is given to ships in other games...

Shipname:

The Lovebus

featuring

Captain Cock

Commander Titts

Lieutenant Boob

That never gets old for me

Got the first Engi ship, saw the two engi, one human compliment, and realized the next move was obvious.

Engi Crew:
Tom Servo
Crow

Human Crew:
Mike

Ship Name:
SatelliteOLove

And true to form, Crow is now my highest ranking Weapons officer. They were kicking ass all across the galaxy until Pearl caught up in a stacked Fighter in the same jump that Servo mysteriously disappeared.

Figures there'd be more Red Dwarf fans here... Every time I start with an Engi, he has to be named Kryten.

For some reason I typically name female humans Holly instead of Kochanski though. Even though there was a "male" Holly and he/she was the ship computer...

Sometimes I try to theme it based on the crew type. For Rock crews, they get named after action hero/wrestler rocks (Sly Stalagmite, The Rock, Arnie Swartzstein).

Haven't figured out a good Mantis naming scheme yet. So far I've just Mantis-ised the Red Dwarf crew (e.g. Rimmzzer, Lizzter, etc.).

Damn good naming schema here! Allow me to present my own, the various and expendable ships and crew of Starfleet.

Ship Name: Constellation, a sister ship of the Enterprise destroyed in the episode The Doomsday Machine.

Pilot: Kaplan, killed on Gamma Trianguli VI in the episode "The Apple."
Weapons: Carlisle, a redshirt killed by Nomad in the episode "The Changeling."
Engines: Leslie. From Memory Alpha: "During a planetary survey of Argus X on stardate 3619.2, he was killed by the dikironium cloud creature after it had drained all the red blood corpuscles from his body. He was revived by stardate 3620.7 and soon returned to active duty."
Shields: Hendorff, killed on Gamma Trianguli VI in the episode "The Apple."