The Greeks referred to Palestine as part of Syria* and the Romans referred to the administrative unit as Judaea until the second century A.D. Earlier, Provincia Judaea had been made an annex of Syria under Augustus (r. c. 31 B.c. - A.D. 14) becoming part of Provincia Syria. Then, in the second century the Emperor Hadrian (r. 117-138) renamed it Palaestina. It is from Palaestina that we get the name Palestine.
*There is controversy here over whether the same area we moderns think of as Palestine was sometimes called Palestine by the Greeks. Hadrian did not just pull the name Palestine out of thin air. There was an historical reason Hadrian named the province Palaestina. Herodotus 3.5.1 writes:ἀπὸ γὰρ Φοινίκης μέχρι οὔρων τῶν Καδύτιος πόλιος ἐστὶ Σύρων τῶν Παλαιστίνων καλεομένωνIf this topic interests you, please consult:
the country from Phoenicia to the borders of the city Cadytis [Gaza] belongs to the people called the Palestine Syrians
Perseus for the Greek/Rawlinson translation
Φοίνικες δὲ καὶ Σύροι οἱ ἐν τῇ Παλαιστίνῃ καὶ αὐτοὶ ὁμολογέουσι
The Phenicians and the Syrians who dwell in Palestine
- "Palestine and Israel"
David M. Jacobson
Bulletin of the American Schools of Oriental Research, No. 313 (Feb., 1999), pp. 65-74
- "Palestine: On the History and Geography of a Name"
The International History Review, Vol. 2, No. 1 (Jan., 1980), pp. 1-12