1st-cent. CE: Aramaic Scroll of Antiochus: "…In the twenty-third year of his (Antiochus Eupator) reign, in the two-hundred and thirteenth year of the rebuilding of this, God's house (Temple), he put his face to go up to Jerusalem. He then answered and said to his nobles, 'Do you not know that the Jewish people in Judea, between us, they do not worship our God, nor do they practice our customs, and they leave off from following the king's religion for their own religion,' etc."
c. 129 or 135: Syria Palæstina was a Roman province between 135 and about 390. It was established by the merge of Roman Syria and Roman Judaea, shortly before or after the Bar Kokhba Revolt. There is only circumstantial evidence linking Hadrian with the name change and the precise date is not certain. The common view that the name change was intended "sever the connection of the Jews to their historical homeland" is disputed. Zachary Foster in his Princeton doctoral dissertation wrote that there is a “paucity of direct evidence around who made the change, when and under what circumstances”, and that it may be that Hadrian did not “rename” the country but simply “called the place what it was called”.Louis Feldman argues prior to change of province name the term was used to refer to the coastal region associated with the Philistines and that first century authors differentiated Judea from Palestine.
189 CE: The Mishnah: "Three countries are to be distinguished in what concerns the law of removal [of seventh year produce once the growing season has past]: Judea, beyond Jordan and Galilee."
392: Epiphanius of Salamis, On Weights and Measures: "So [Hadrian] passed through the city of Antioch and passed through [Coele-Syria] and Phoenicia and came to Palestine — which is also called Judea — forty-seven years after the destruction of Jerusalem."
c. 1130, Fetellus, "The city of Jerusalem is situated in the hill-country of Judea, in the province of Palestine" 
1746: Modern History Or the Present State of All Nations: "Palestine, or the Holy Land, sometimes also called Judea, is bound by Mount Libanus on the north; by Arabia Deserta on the east; by Arabia Petrea on the south; and by the Mediterranean Sea on the west"
The name occurs multiple times as a geographic region in the Hebrew Bible, in both Hebrew and Aramaic:
^Feldman 1990, p. 19: "While it is true that there is no evidence as to precisely who changed the name of Judaea to Palestine and precisely when this was done, circumstantial evidence would seem to point to Hadrian himself, since he is, it would seem, responsible for a number of decrees that sought to crush the national and religious spirit of thejews, whether these decrees were responsible for the uprising or were the result of it. In the first place, he refounded Jerusalem as a Graeco-Roman city under the name of Aelia Capitolina. He also erected on the site of the Temple another temple to Zeus."
^Jacobson 2001, p. 44-45: "Hadrian officially renamed Judea Syria Palaestina after his Roman armies suppressed the Bar-Kokhba Revolt (the Second Jewish Revolt) in 135 C.E.; this is commonly viewed as a move intended to sever the connection of the Jews to their historical homeland. However, that Jewish writers such as Philo, in particular, and Josephus, who flourished while Judea was still formally in existence, used the name Palestine for the Land of Israel in their Greek works, suggests that this interpretation of history is mistaken. Hadrian’s choice of Syria Palaestina may be more correctly seen as a rationalization of the name of the new province, in accordance with its area being far larger than geographical Judea. Indeed, Syria Palaestina had an ancient pedigree that was intimately linked with the area of greater Israel."
^Foster, Zachary (November 2017). "Southern Syria". The Invention of Palestine (thesis). Princeton University. pp. 103–110. ISBN9780355480238. Docket 10634618. Retrieved 9 February 2018. The Roman Emperor Hadrian is claimed to have replaced the district of Judaea with Palestine to erase the land’s Jewish identity after crushing the Bar-Kokhba revolt in 135 AD, what we might call the erasure hypothesis… Historians do not believe that Hadrian preserved the administrative boundaries of Judaea and simply rename the province Palestine. Instead, the consensus is that the district was abolished altogether and replaced not with Palaestina, but with Syria-Palaestina… But there are also some major problems with the erasure hypothesis. It assumes that Palestine was not already the name of a region that included Judaea. If it was, then how could Hadrian have changed the name to Palestine?… But Palestine did not emerge forth from Judaea, it had coexisted with it long before it was putatively changed to it. Herodotus (d. 425 BC) was the first on record in the Greek world to use the term Palestine. The prevailing theory is that he adopted the term from Aramaic—both because Aramaic was the closest thing the Near East had at that time to a lingua franca and because Middle Aramaic, a Semitic language related to Hebrew, had a form of that word—Pi-li-s-ta'in—closest to Herodotus’s Greek usage… Others writers… used the term before 135 CE, and they included Judaea in it. So, Palestine included Judaea a long time before Hadrian said it included Judaea. We have a plausible motive for the change without knowing anything else about Hadrian: he called the place what it was called. Interestingly, Hadrian… admired Greek aesthetics, art and philosophy and even changed provincial names to Greek ones elsewhere in the Empire as symbolic acts of restoration. This included the city of Antigonea, called that by the Macedonian king Antigonus Doson, which he changed to Mantinea—its Greek name during the time of Sparta’s prominence; the city of Sepphoris, which was renamed Diocaesarea in Hadrian’s honor in 130; he renamed Jerusalem Aelia Capitolina—to remind Christian Roman dissenters that it was Aelius Hadrianus—i.e. himself—who held power in Jerusalem. It’s plausible he renamed Judaea not because he wanted to give BDS a head start, as Malcolm Hoenlein believed, but rather because he loved the Greeks—and he thought the Greeks called the place Palestine… The decision to change the name to Palestine may have been a banal bureaucratic choice. The whole affair might have passed without anyone thinking there was anything vengeful about the change. This seems plausible, especially given the paucity of direct evidence around who made the change, when and under what circumstances. If the administrative reorganization was indeed banal, then we might have expected both names to have persisted after the change, which is exactly what happened.
^Louis H. Feldman (1996). Studies in Hellenistic Judaism. Brill. p. 553.