Yes and No.

USS Hornet, CV-8, did sink at the Battle of Santa Cruz.

USS Hornet, CV-12, was renamed in honor of the sunk CV-8 and still exists. She is a museum ship in Alameda, CA

USS Hornet served only in the second world war. The CV-8 and the CV-12.

USS Hornet (CV-8), launched the Doolittle Raid in 1942, fought at the Battle of Midway, and was sunk at the Battle of the Santa Cruz Islands on 26 October 1942.

USS Yorktown (CV-5). She was the lead ship of the Yorktown-class and sister ship to Enterprise (CV-6) and Hornet (CV-8)

CVN-65 is the 65th Fleet Carrier designated to be built; some carriers were assigned a number and never buillt, consequently their number was skipped, so there were not 65 aircraft carriers built when #65 was constructed. CV-1 was the USS Langley (sunk during the time frame of the Battle of the Java Sea campaign); CV-2 was USS Lexington (sunk at the Battle of Coral Sea); CV-3 was USS Saratoga (sunk during atomic bomb testing in 1946); CV-4 was USS Ranger (only used in the Atlantic during the war, was deemed to risky to assign her to the Pacific/ulitimately scrapped); CV-5 USS Yorktown (sunk at Midway); CV-6 USS Enterprise (the USN's most decorated warship/scrapped); CV-7 USS Wasp (Sunk during the battle of Guadalcanal); CV-8 USS Hornet (sunk during the battle of the Santa Cruz Islands); etc. CV-63 was the USS Kitty Hawk, CV-64 was the USS Constellation, etc.