Well, ship designators have been frought with all sorts of issues for ever and ever. First off, somebody decided it had to be at least two letters, which has lead to odd doublings ever since. But, most of the doublings make a slight sense--BB, DD, SS, etc.
CV comes from (aircraft) "carrier" "heaVier-than-air". Recall that the USN had experimented with lighter-than-air carriers in Macon and Akron. That "V" still occurs in the squadron designations to this day.
Cruisers were going to be CA, CB, CC; but the original size split was only heavy and light. That newfangled auxillary for toting aircraft around was catching on, and it used a "C" as well. Somehow, the split was rendered to be CA & CL (to then catch a monkeywrench with the CLAAs).
Where it all goes "thick" (to borrow the expression from my brit friends) is in the Auxillaries. Nothing like "leaving off" the A part to relly muddy the issue <g>.
Then, the poor amphibs . . . "well Deck" gets turned into "Dock" (not helped with US Army designations only vaguely similar, if widely published).
Almost simpler to ask about a specific designation than all of them <g>.