There are specific rules which USN ship names must follow - or at least that's how it used to be but now it seems like "any ship is to be named as however the hell the Sec of the Navy feels like it."
The consolidation of many ship types down to a few (battleships, battlecruisers, "large cruisers", light cruisers, heavy cruisers, anti-aircraft cruisers, light guided-missile cruiser, heavy guided-missile cruiser, frigates, destroyer leaders, destroyer escorts, patrol frigates, patrol gunboats, submarine chasers, anti-submarine carriers, attack carriers, conventional carriers, etc = frigates, destroyers, cruisers, carriers and this new "Littoral Combat Ship" thing) seems to be a major culprit. The old system used to be this, circa about WWII:
Battleships = states
Battlecruisers = significant battles in USN history, names recycled specifically from historic USN sailing vessels
Aircraft Carriers = significant battles in USN history, names recycled specifically from historic USN sailing vessels
Large Cruisers = US territories
Cruisers, all other types = cities
Frigates = cities or USN captains, admirals or personnel who have died in the line of battle
Destroyers/Destroyer Escorts = USN captains, admirals or personnel who have died in the line of battle
Patrol Frigates and Gunboats = cities
Submarine Chasers and smaller = hull numbers only
Submarines: fish species
Axillary Replenishment vessels = Rivers
Axillary Repair Vessels = significant American citizens (i.e. civilians) who have made important contributions to modern invention, Roman dieties
Tugs = Native American tribes
Axillary offensive vessels impressed into service = retention of civilian name
And note that even when such a "clear and defined" list is available, things are still derp'd the eff up. Look at how there are multiple possibilities for one type of vessel, or how multiple types of vessel overlap the same category. The reason why both battlecruisers and aircraft carriers ended up with the same naming convention was because the first carriers the USN had were converted battlecruisers and the naming convention, with very few exceptions, stuck with it all the way up to the launching of Forrestal (the sole exceptions I can think off the top of my head were Langley, named after the arguable birthplace of the floatplane and Shangri-La which was after the codename for Hornet during the Doolittle Raid). Even United States would've been named after a War of 1812 sailing vessel. And since the USN never had any battlecruisers proper that one's forgivable.
But there are other WTF things in there too. Frigates/Destroyer Leaders were a gray area because we've never actually had any proper "frigates" or "destroyer leaders" in commission until after WWII, but we've had ships from cruisers (Atlanta) to destroyers (Porter) that fit the role and are sometimes described in literature as being "functionally equivalent to destroyer leaders or frigates". But once again that's just semantics. But WTF is up with patrol frigates and gunboats? Why does a 600 ton or less vessel follow the same naming convention as vessels from 10,000-20,000 tons? WTF, USN? Y U KNO LIEK TACOMA if that city just got a 400 ton boat with three 75mm cannon onboard (outgunned and outweighed by a DE for goodness sakes) vs. Boston which was a 15,000-ton 8-inch gun monster?
And then you get things that are different but have the same name. I'd like to name an oiler after the Arkansas River...oh, wait. Oopps. And that's how we ended up with a 103-foot armed yacht named USS California.
And things just get more complicated from there, especially when you start contracting ship types. Let's look at ships that were actively being built from 1950 to 1975:
Aircraft Carriers: battles, historic USN sailing ships, personnel (KIA, distinguished retired, or distinguished civilian service people with service records)
Frigates and destroyer leaders: personnel
Nuclear frigates: personnel, states
destroyers, destroyer escorts and misc. escorts: personnel
Attack Submarines and Cruise Missile Submarines, conventional, nuclear or otherwise: fish species
Ballistic Missile Submarines: Significantly historic Americans regardless of naval or military service (I don't think noted pacifist George Washington Carver would've been very thrilled having a nuclear doomsday machine named after him)
Amphibious transports and amphibious auxiliaries: cities, battles specifically involving US Marines
Auxiliary replenishment ships: cities, personnel, rivers, adjectives related to supplying stuff, bum&!)%! if I know
Tugs: Native American tribes
Auxiliary repair ships: significant inventors
Note that battleships and cruisers were not under construction at this time (from 1950 to 1975 all USN cruisers in service were commissioned prior to 1950, including vessels rebuilt and recommissioned).
Look at all those ship types that are no longer present - and what's especially important is look at all those ship types that now include people. Now we really are on the first step towards "whatever the hell people felt like naming it, likely based on who gave us the most money."
Things got really fun after the 1975 Classification Realignment up until 2000 (includes all types in commission):
Aircraft carriers: Famous USN sailing ships, people, people not even dead yet!
Cruisers: states, cities, personnel
AEGIS cruisers: battles
Destroyers: personnel
Frigates: personnel
Attack submarines: cities, personnel
Ballistic missile submarines: states, personnel
Auxiliaries, all types excluding tugs: rivers, cities, random words and adjectives, personnel
Amphibious transport assets: Marines battles, cities, famous USN sailing ships
Look at how the list is getting shorter - and while I wouldn't say it's all over the place, it's getting pretty damn close. And once again, the increasingly prominent thread, ships named after people, and increasingly people with political connections (usually people who happened to have been figureheads of one of the two major political parties).
And since about 2000 everything just got bum&*)(!'d. This time I'll include all ships currently in commission specifically as of Leap Day 2012 (the day of this posting):
Aircraft Carriers: Enterprise, a few admirals, Dead Presidents (that happen for the most part be major cultural figureheads for one political party or the other), recently deceased people who happen to have major political connections, people who are still alive who happen to have major political connections
Cruisers: major battles (all commissioned before the current environment of naming ships after the politically connected)
Destroyers and Frigates: personnel who served significantly or were KIA with the USN (this one's too much of a political hot potato to change)
Littoral Combat Ship: cities, random words, whatever, who the hell knows
Attack submarines: cities, states, people with significant political connections
Ballistic missile submarines: states, people with significant political connections
Amphibious assets: battles, historic USN sailing vessels, cities, states, determined by dart board, people with significant political connections
Auxiliaries, all types except tugs: wealthy people, politically connected people, people whose names represent an obvious "feel good" choice for the Sec of the Navy that day
Yeah, now we've reached the point where we can really say that a ship's name is determined by whatever the hell the Sec of the Navy felt like that day. But that trending thread is still there. So now we can safely say in the future:
Any and all commissioned U.S. Navy vessels: determined by campaign finance donations
...even you doubters who say I'm just being too cynical admit there's a lot of truth to it.
As for the British Navy, well, they've been outplaying us on the randomness meter for centuries. I don't have any idea what the hell an "Ark Royal" is (other than Drake's flagship against the Spanish Armada) or how a destroyer is named "Brave" and a carrier "Illustrious" or how Mountbatten ended up on "HMS Kelly." So in the end if you're looking for naming suggestions for an AU it's really up to you as all navies invent their own rules and even then hardly ever play by them anyway.
Hell, in my AU, the navy thinks its Disney
