This idea that ship classes are invariably named after the first ship of the class built is an invention of the spinoffs, though, isn't it? IIRC, TOS had "DY-100" and "DY-500" class freighters. And wasn't Christopher Pike crippled in a training accident on board a "J-class starship"? I'd be surprised if we ever saw an "S.S. DY-100" or the "USS J."
Admiral Grumby sails in from the South Pacific, fires a broadside and demasts the thread. Now, that's seamanship. Looks like I have to surrender my sword.
Yes, it appears the "J-class starship" is the only TOS onscreen evidence that could suggest how to distinguish starships from one another.
Just as the don't say "Earth-class" but "M-class" for planet classifications. I definitely prefer X-class over that "Mark IX/01" nonsense that obviously was a reference to the primary phaser and not to the type or model of ship.
Bob