Actually, CVN is: Cruiser aViation Nuclear powered. (Carriers were originally considered have a scouting/screening role like Cruisers. And they couldn't be CA "Aircraft Cruiser", because at the time, CA was "Armoured Cruiser".)
U.S. Navy aircraft carriers intended to operate with the main fleet were numbered in the "CV" series, which was originated as part of the cruiser ("C") group of designations. During and after World War II, ships in the CV series were frequently given modified designations, including CVA (attack aircraft carrier), CVAN (nuclear-powered attack aircraft carrier), CVB (large aircraft carrier), CVL (small aircraft carrier), CVN (nuclear-powered aircraft carrier), CVS (anti-submarine warfare support aircraft carrier) and CVT (training aircraft carrier). All of these expanded designations were numbered in the original CV series.
When I served aboard the Enterprise she was a "CVAN"... I don't know when the changed it.