Contemporary class designations include: Frigate FG and various subtypes; Destroyer DD and various subtypes such as DDn for Destroyer, Nuclear; Light Cruiser CL, and again various subtypes, such as Guided Missile, Light or Heavy Cruisers; Heavy Cruiser CA; Battlecruiser CB, this is a very misleading class, and many nations have their own definitions. The first Battlecruisers were essentially much faster Heavies. Some nations converted their old Dreadnaughts to CB's by installing more powerful engines, better guns, etc. To some nations, such as the Soviet Union during the Cold War, a CB was a class of ship between a CA and a Battleship. I personally prefer to use that definition when CB's applied to FS; Battleship BB; Carrier basic designation is CV for fixed wing carriers, and CH for rotary wing or VTOL carriers. Most US carriers are "CVN's" for Carrier, Fixed Wing, Nuclear.
Frigates are designated "FF", Corvettes are "FFL" (presumably the L is for "light").
Battlecruiser designation, since you appear to be using the USN convetions, is
NOT CB. This is the designation for "Cruiser, Large" (B is used to indicate, presumably, big; the Midway-class were originally called CVBs for example). The Alaska-class ships were not battlecruisers, which implies they were designed to stand in main battle line and shoot it out with similar ships, but heavy cruiser hunters, intended for use in the large empty areas of the Atlantic and Pacific hunting down ships like the
Prinz Eugen which had broken out to go merchant raiding. The designation used for the only class of battlecruisers the US ever laid down, and they were not completed as such, was CC.