See, I can't think up a good name for a colonisation ship designed to be able to manage a cross-galactic travels, of a size of smaller country.
Ideas?

Spelljammer
Trafalgar
Vaså

Endeavour or Discovery are always good choices.

=P
Name it Khaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaan!
Add more a's for extra emphasis.
But seriously though, whenever I want some kind of grand ship, the first name that comes to mind is Titanic. But you might not want to use such an ill-fated name.

Heh I'm just imagining a flyby shot like the star destroyer at the start of A New Hope only with the name stretching from bow to stern

And the first thing that came to my mind was....
KHAAAAAAAAAAAAAAN!;P
Lady Juliana is also a nice name for a breeding ship..;P

Providence
Eternity
Liberty
Triumph
Leviathan
Majestic
Defiant
Intrepid
Dauntless
Infinity
Gotta love the old thesaurus

Non-original
Galactus
Galactica
Dawntreader
Apollo
Icarus
original;
Adamant
Vagabond
Seafarer

Lusitania (eh,eh)
Colonus
Forlorn
Pilgrim
Prosperity
Serendipity
Gallivant

I lick these two. And Tiny is sure to become a nickname :D
And Khaaaaaaaaaaaaaaaaaaaaaaaaaaan is, of course, awesome, however I want it to have this majestic feel.

... Serenity after bombing? :D

Sentinel
Defender
Guardian
Shield
Paladin
Champion
And if you don't mind the association with a mass-murdering space machine you could always go with Sovereign

Who's to say your colonists won't stumble upon some awesome planet while looking for another ? ;)

Some other ideas:
Prophet
Hand of Destiny
Omen
Asylum
Vae Victus :P
Edit: Most of these names can be enhanced with adjectives ;).

The Endar Spire

Call it the B-Ark and put all of the planet's insurance salesmen, personnel officers, marketing executives, management consultants and telephone sanitizers on it.