The name Palestine refers to a region of the eastern Mediterranean coast from the sea to the Jordan valley and from the southern Negev desert to the Galilee lake region in the north. The word itself derives from "Plesheth", a name that appears frequently in the Bible and has come into English as "Philistine". Plesheth, (root palash) was a general term meaning rolling or migratory. This referred to the Philistine's invasion and conquest of the coast from the sea. The Philistines were not Arabs nor even Semites, they were most closely related to the Greeks originating from Asia Minor and Greek localities. They did not speak Arabic. They had no connection, ethnic, linguistic or historical with Arabia or Arabs.

The name came into use in the thirteenth century BCE, for the "Sea Peoples" who migrated from the region of the Aegean Sea and the Greek Islands and settled on the southern coast of the land of Canaan. There they established five independent city-states (including Gaza) on a narrow strip of land known as Philistia. The Greeks and Romans called it "Palastina".

The above answer is a straight copy-paste from:
http://www.palestinefacts.org/pf_early_palestine_name_origin.php

The term “Palestine” is believed to be derived from the Philistines, an Aegean people who, in the 12th Century B.C., settled along the Mediterranean coastal plain of what is now Israel and the Gaza Strip. In the second century A.D., the Romans crushed the revolt of Shimon Bar Kokhba (132 CE), during which Jerusalem and Judea were regained.

Three years later, in conformity with Roman custom, Jerusalem was “plowed up with a yoke of oxen” and renamed Aelia Capitolina. Judea (the southern portion of what is now called the West Bank) was renamed Palaestina in an attempt to minimize Jewish identification with the land of Israel. The Arabic word “Filastin” is derived from this Latin name.

Since the defeat of Israel's third rebellion against Rome in 135 AD the land of Israel has been dubbed "Palestine." It is a name that been perpetuated in both secular and biblical history.

In his article, "When Palestine Meant Israel," (Biblical Archaeology Review, May/June 2001, Vol 27, No. 3, pp. 42-47), David Jacobson brings some interesting insight into the argument regarding the origin of the name Palestine. In the article, he admits the "phonetic similarity between Palaistine and Peleshet, the Hebrew word for the "land of the Philistines."

The designation "Palestinian" did not come into vogue until the 1967 Six-Day War. Three years prior to the '67 war, the Palestinian Liberation Organization was formed to liberate "Palestine," which included both Israel and Jordan.

PALESTINE IS TRANSFORMATION OF PHILISTINE , THE ANCIENTS HABITANT OF THE HOLY LAND

When the Romans took over Israel and destroyed the Temple in ancient times they renamed the country Palestine.