I love the shipbuilder - naming and adding class descriptions is a great example of a relatively cheap feature that makes a good feature like the shipbuilder GREAT!
Early in the game - I don't usually build many offensive ships - should a war arise, my ships are usually named after the race they'll be sent into battle against (Korx-busters, etc). Until I settle in military technology wise -- only colony, survey and constructor ships get class names. I don't do "class upgrades" that is, each tech-tiered ship gets its own class name.
For constructors, I use class names like DaVinci and Edison.
For colony ships - Mayflower, Sooner, Pilgrim.
For survey ships - Hawking, Galileo, Copernicus.
For freighters - famous sci-smuggling ships... Firefly, Millenium Falcon, etc.
Later in the game - I go all over the scifi map, usually in groups (i.e., 1 missile-focused, 1 laser-focused, 1 railgun focused for each size).
For instance - a huge class might have 3 ship types: Deadalus, Odyssey, Prometheus. Or Sovereign, Galaxy, Defiant. Or Aurora, Orion, etc. Or Galactica, Mercury, etc. I also dip into Greek gods (usually have a trio around Apollo, Archimedes, Zeus), as well as a fondness for Royal Navy naming conventions (Colossus, Neptune, Majestic). Famous admirals/generals (Eisenhower, Perry, Nelson), famous battles (Trafalgar, Midway, etc) also get used. Troop Transports always get names like Normandy, Iwo Jima, Tripoli.
I play long games on big maps - and will even try to wait with serious classifications until I'm tech'ed out... by which time, I'm sometimes creating 40 or more classifications. I'll create special planet defense ship classes (no engines), special escort ship classes (fast, defense-intensive ships), classes specifically designed for starbases defense.