Note: This post only covers combatant vessels.
Aircraft Carriers
Fleet & Light carriers (CV & CVL)
Named after famous old USN ships & famous battles
Example: USS Saratoga (CV-3)

Escort carriers (CVE)
Named after U.S. sounds & bays, WWII naval battles
Example: USS Gambier Bay (CVE-73)

Battleships (BB)
Named after States
Example: USS Iowa (BB-61)

Cruisers
Large cruisers (CB)
Named after U.S. Territories & possessions
Example: USS Alaska (CB-1)

Heavy cruisers (CA)
Named after large American cities & towns
Example: USS Northampton (CA-26)

Light cruisers (CL)
Named after medium American cities & towns
Example: USS Omaha (CL-4)

Destroyers & Destroyer Escorts (DD & DE)
Named after distinguished USN/USMC officers & men
Example: USS Samuel B. Roberts (DE-413)

Submarines (SS)
Named after fish & other sea creatures
Example: USS Tang (SS-306)

Submarine Chasers (PC)
No naming convention, given numerical designation
Example: USS PC-815

Minecraft
Minelayers (CM & DM)
Named after old monitors of the USN
Example: USS Terror (CM-5)

Auxiliary Minelayers (ACM)
Named after obstructions and fortifications
Example: USS Barbican (ACM-5)

Minesweepers (AM, AMc, & DMS)
Named after birds or abstract qualities
Example: USS Osprey (AM-56)

Patrol Craft
Gunboats & Frigates (PG & PF)
Named after cities & towns
Example: USS Tacoma (PF-3)

River Gunboats (PR)
Named after islands
Example: USS Panay (PR-5)

Converted Yachts (PY, & PYc)
Named after precious & semiprecious stones, general words
Example: USS Ability (PYc-28)

Motor Torpedo Boats (PT)
Given numerical designations
Example: PT-105

References
Stubblebine, D. (2009, March). Naming Conventions of US Navy Ships, 1940-1945. Retrieved from https://ww2db.com/other.php?other_id=35