This appears to be an error in filming. In an earlier draft script, Kirk was apparently told the creature's name in a deleted scene.
KIRK: (continuing) Come—join us. You—must have a name.
TOMMY: (defiantly) He is Gorgan. He is our friend—and he is all powerful.
And in the episode's official novelisation (itself based on the final shooting script), ...
It is never directly shown how Kirk knew the creature's name. An early draft of the script did include a deleted scene in which Kirk asked what the creature was called and was informed by Tommy that it was Gorgan, but in a bit of sloppy editing the scene in question occurred after Kirk already referred to it by name.
There were in fact a few episodes that had their plots drawn from material rejected for Star Trek: The Original Series, primarily episodes that served as sequels to previous ones. The episodes More Troubles, More Tribbles, The Magicks of Megas-tu, Once Upon a Planet, and Mudd's Passion were all originally conceived as episodes of The Original Series, though ...
While not 'the killers of today'¹, the common cold seemed to remain a problem until the mid-24th century.
In a rough progression of broadcast (not chronological and not complete):
ST:TOS Dr. Leonard McCoy
ST:ENT Various personalities
ST:DIS Saru and Linus
See the full Memory Alpha - Common Cold page for more info. I think I've regurgitated ...
For additional context, the full correspondence wasn't about a single episode, but the overall direction of the two main leads, as the correspondence occurred between Season 1 and Season 2.
Asimov recommended ways that Shatner could still stand out as the primary lead:
The problem, then, is how to convince the world, and Mr. Shatner, that
Mr. Shatner ...
According to the showrunner Michelle Paradise, her name is Una
From the interview with the ST:DIS co-executive producer:
TREKCORE: Rebecca Romijn’s Number One went by ‘Commander’ or simply
‘Number One’ for most of her time on-screen, but it sounded like Pike
did call her ‘Una’ one time during the finale — the character’s name
from the Star Trek tie-...