Why is the Roman emperor Titus known as Titus? Usually we don't refer to a Roman by his first name (praenomen). And it's not as if it serves to distinguish him from his predecessor (and father) or his successor (and brother) - they were also named Titus! How did this come about - and when?
Romans weren't very concerned about unique names for just about anyone. In the Late Republic, Fathers, sons, grandsons had about three between them per family. All girls were just named after the family with a feminine ending. i.e. Julia --> "Julian Girl".
In the case of Vespasian's family, the second son had the name Domitianus added to the standard names pack and thus was known to history that way. Father and eldest son having the same name didn't seem to bother the Romans then. I haven't looked in Tacitus or Seutonius in the original Latin so I can't say now if the original historians called both Vespasian and Titus as "Titus Flavius". I know that Caligula was known as Emperor Gaius Julius Caesar in his time, not by his current nickname.
Edit: Seutonius in Latin titles his chapters "Divvs Titus" and "Divvs Vespasianvs" and "Caligvlae". In the text for all except Caligula he uses the same name inside. He uses C. Caesar in the text then.
A modern translation will give the standard names to avoid confusion for moderns, who aren't experienced with Roman quirks, namewise.