🔼The name Latin in the Bible
The name Latin (Λατιν) doesn't occur in the Bible; the two Biblical references to the Roman language tell of Ρωμαικος (Romaikos; Luke 23:38) and Ρωμαιστι (Romaisti; John 19:20). But the Latin Vulgate translated both these occasions with latin, and most modern translations stay close to the Latin version, especially where names are concerned. A few Greek compound words that contain the segment latin (such as Λατινοηθησ, Latinoethes, meaning following Latin customs) demonstrate that the word Latin was surely known and used in the Greek world of the first century.
The name Latin belongs to the language which was spoken in Latium, which in turn was peopled by the Latins, which was a minority group in Iron Age Italy (which wasn't called Italy until the start of the Roman Empire in the first century BC). These Latins had come from the east, with a wave of Indo-European settlers who displaced much of the indigenous European peoples, such as the Celts, who were driven north of the Alps.
Despite some inevitable frictions between people groups, the cultural consistency of the Italian peninsula up until (and obviously after) the Roman conquest was remarkable. Rome was originally a small Latin city state, close to the much larger territory of the Etruscans. Rome's rise to power was initially opposed even by its fellow Latin tribes. The ensuing Latin War was won by Rome, and Rome's subsequent realm of control is a remarkable testament to the power of synchronicity versus that of sheer numbers.
Latin became the lingua franca of millions of non-native speakers, and although it never truly replaced Greek (hence the Greek and not the Latin New Testament), its amazing conquest was not repeated until small bands of displaced Saxons and Jutes journeyed from Germania to Britain when the Romans evacuated it in 450 AD, flooded it with their language, which was more than a millennium later adopted as the national language of the American colonies, and is presently the lingua franca of the world: English.
🔼Etymology of the name Latin
It's no longer clear where the name Latin comes from, but linguists propose that it comes from an ancient proto-Indo-European root stela- (Sanskrit: star-; hence the English word "sternum"), which is thought to have meant to spread or extend. This same root gave the Latin language its familiar adjective latus (in old Latin stlatus), meaning wide, from whence comes the Latin word latitudo and thus our English word "latitude".
The name Latin would thus have been applied to people living on flat plains, as opposed to mountains. In Hebrew exists a similar verb, namely רחב (rahab), meaning to be large or wide, which would interestingly tie Biblical characters such as Rahab and the town of Beth-rehob to the Latin language and thus to the wisdom tradition expressed in Latin.
The name Latin means Spacious in Latin, or when we follow the many nuances of the adjective latus: Lavish, Copious or Exhaustive or even Proud.