According to the Mishna, it was the Falasteen (Philistines) who welcomed and cared for the Jews after 40 years in the desert.

Yes, there were later wars and land grabs by Judah against the Falesteen. (The more things change...) The Sages excused this perfidity by asserting (without textual or other evidence) that there were two peoples called Falasteen.

Palestina or Syria Palestina was a name the Romans gave the whole region when they made it a Provincia.

Because the Falesteen (Palestinae in Latin) had been the most loyal to Rome. More loyal than Judah, Ysrael, Samaria, the Canaanite city-states or the Phonecian city-states, all of whom became parts of Roman Palestina.