Redshirts always have so many questions.

They called Starfleet like four different things before they settled on Starfleet.

Given that was the very first filmed episode (as a second pilot) it can be forgiven (The Man Trap was the first aired). I can't find a reason for picking "T" later on in the series, but it sounds better than "R" when announcing his full name to an alien ship. "Tiberius" didn't even come along until a later animated episode, and still wasn't canon except to fans until it was used in The Undiscovered Country.