Latin is the name that the Romans themselves used for their language, which was the local Italic language/dialect that was spoken in the region of Latium, a collection of settlements in the lower Tiber valley. It was not the only Italic language; a Roman would have little difficulty conversing with a resident of, say, Tusculum or Lavinium, but would have more difficulty with other branches of Italic, as for instance the Oscan of the Samnites (an example being that the Latin "quid" for the interrogative "what" is instead rendered in Oscan as "pid" -- the relationship is visible but the languages are certainly different). Rome was one of the Latin cities, and became the predominant one (not always peacefully), with a victory over an alliance of Latin cities yielding Rome supremacy over the region from 338 BC. So, in that sense, insisting on calling the language "Roman" would be like insisting on calling English "Londonish," although that isn't a particularly fair comparison since the ancient Romans had a concept of the city-state than the medieval English did not.

Interestingly, the term Latin was used by the Romans through the Republic and into the Empire for a sort of partial Roman citizenship; the "Latin right" or "Latin citizenship" described people and municipalities that possessed some, but not all, of the rights of Roman citizens, and the legal framework was extended to this conferring of partial citizenship to groups that had nothing to do with Latium, as for example a grant of the ius Latii to Spain by the emperor Vespasian, per Pliny the Elder's Naturalis Historia.