There's a 1980 movie called "The Final Countdown" in which the USS Nimitz is time warped back to December 6, 1941. Charles Durning plays a US Senator who is rescued at sea and brought aboard the Nimitz and asks that very question, "What is a US Navy ship doing named after a serving Admiral?" The story line is kind of hoakey, but like "Top Gun" a few years later, was a good show of US Navy firepower.
Had it not been for the A-Bomb, there's a good chance the USS Coral Sea would have played a role. It along with the Midway and FDR were a new class of super-carriers that totally outclassed the Essex class flat tops that carried the bulk of the war in the Pacific, and arrived just a little too late. Like the A1 Skyraider they were to carry, they all proved their worth well into the Viet Nam war and beyond.
This may explain Hank's confusion.
I wonder if there'll be any references to Admiral Kirk Douglas in his upcoming miniseries?