Kirk’s middle name, Tiberius, was established in the TAS episode, “Bem”. Prior to that, the only indication of what his middle name might be was in the second pilot, “Where No Man Has Gone Before” when Gary Mitchell created a tombstone reading ”James R. Kirk”.
While David Gerrold canonised the "T" as standing for "Tiberius" in "Bem", we did know that his middle name started with the letter "T" as far back as "Mudd's Women" IIRC. You undoubtedly already knew this, but the way this particular connection was worded suggested that the "T" also first appeared in "Bem", when it had been established early in TOS.
Incidentally, but non-canonically, in Gene Roddenberry's novelisation of The Motion Picture, he has Kirk write, in "Admiral Kirk's preface" to the novel, that:
Tiberius, as I am forever tired of explaining, was the Roman emperor whose life for some unfathomable reason fascinated my grandfather Samuel.
And quoting from that same preface just for shits and giggles and to proffer today's insight into the mind of Eugene Wesley Roddenberry:
I received James because it was both the name of my father's beloved brother as well as that of my mother's first love instructor.
While David Gerrold canonised the “T” as standing for “Tiberius” in “Bem”, we did know that his middle name started with the letter “T” as far back as “Mudd’s Women” IIRC. You undoubtedly already knew this
I actually was not aware of that! Interesting that “Where No Man Has Gone Before” and “Mudd’s Women” had different middle initials for Kirk considering the later was originally conceived as possible second pilot as well. Too bad “The Omega Glory” didn’t also get in on the game.