Yes, Judah was a person and the land of his posterity was called Judah until the posterity was forcibly and completely removed from that land to Babylonia. The word Jew never really derived from Judah and certainly did not exist during the Roman times as I will explain in the following paragraph..

Rome referred to the region as 'Judea' from the Latin 'Iudaea', which is derived from the Greek 'Idumea'; "land of Edomites" and those people of the region as 'Judeans'. From the time of conquest by Alexander the Great, the region was called Idumea. The influence of the Greeks in the entire Levant was so culturally dominating that the written paleo-Hebrew was threatened. As a result, the Greek Septuagint was written in 256 BC. The international language throughout the eastern Mediterranean was koine Greek. Without records, it is plausible that Jesus may have read from the Greek Septuagint. We don't know for sure. Nevertheless, the Romans readily accepted the Greek influence existing there and added their own Latin version. The Romans simply used the Latinized version ('Iudaea') of the Greek 'Idumea'.

Much later the word Jew comes into existence in England in circa 1600s, which coincides with a wave of Yiddish immigrants coming from France and Deutschland. Originally the English term 'Jewry' referred to those immigrants coming from Eastern European people who spoke Yiddish (Ashkenazi). A French derogatory term for 'ghetto' and the Yiddish district of town was called -- 'Jeuerie'; "ghetto", from Anglo-French 'Juerie', Old French 'Juierie' or the later English version 'Jewry'. The word 'Jew' did not exist during the Roman times. Even Pontius Pilate inscribed a title in Latin on the torture stake that properly translated reads - "Jesus the Nazerene King of the Judeans". From the above entymology of the word Judean, we find the plaque was far more derogatory to the death of our Savior than people realize. The real translation is -- "Jesus the Nazerene King of the Idumeans (Edomites)."