When and why was the Holy Land given the name Palestine? What was its name before that?
The Roman emperor Hadrian reigned from 117-138 CE. He rebuilt the ruins of Jerusalem and changed the name of the city to Aelia Capitolina (after his own family name Aelia and an idol of his). After the Jewish revolt under Bar Kochba, which lasted more than 2 years and cost the Romans and Jews enormous casualties, Hadrian forbade Jews to set foot there. Jews continued to live in the Holy Land in places such as Yavneh, Tiberias, Acco and Sephorus. Hadrian also changed the name of the land from Judea to Palestine, after the ancient people called the Philistines, who were the Jews' main enemy in the time of King David. There were no longer any Philistines in Hadrian's time but his purpose in changing the name was not to be historically accurate, but to disconnect the land from the Jews in the public memory and discourage them from ever mounting another rebellion.
Israel was always the name of the Jewish people, but in general, the Bible did not always stick to the modern notion that a people and its land have the same name. For example, in the Bible the Holy Land is almost always called the Land of Canaan, after the Canaanite peoples who lived there before the Jews, although the Jews lived there for 850 years in the Biblical era. The term "Land of Israel" is very rarely found. After the division of the kingdom under Rehabeam and Jeroboam, the southern part came to be called Judea. In Second Temple times, the southern half was called Judea and the northern half was called Galilee. The entire Holy Land is called "the Land of Israel" in Rabbinic writings.