Watching Star Trek (original) season 1 episode 3 "Where no man has gone before"
Late in the episode on the planet where Lt. Comm. Gary Mitchell is battling Capt. Kirk ... the tombstone for Capt. Kirk reads: James R. Kirk, not James T. Kirk. Interesting. I wonder when they changed the middle name to Tiberius?
I am a big Trek Tos fan, to the point of knowing trivia about stuff like this. Anyway, there is an hour or so, two part video on YouTube with Herbert F Solow, one of the producers and writers, that touches on this.
Evidently, Gene Roddenberry had a superstition about using R in the middle names of his characters; hence they used James R. Kirk. As for when they changed it to Tiberius, i do not know. I think he uses T. pretty early in season one. (The first three episodes were all done quickly including "Where no man has gone before." I bet it was sometime soon after that, fwiw.
(Good luck finding the video; it is interesting. it has lots of little nuggets about the formation of the show and about Roddenbery's life and earlier career.) For Example, Sulu was named in honor of Herbert F. Solow.