Actually the name "Palestine" is older. It could go back as far as 1150 BC with an inscription on a temple in Egypt, "Peleset". In 5th century BC, Greek historian, Herodotus wrote of a "district of Syria, called Palaistinê" between Phoenicia and Egypt.
There is a strong similarity between Palaistī́nē and palaistês, the Greek word for "wrestler/rival/adversary", which has the same etymological meaning as the Hebrew word "Israel."
Jacob, in the Hebrew Bible (Old Testament for Christians) had his name changed by God to Israel. Israel means "one who wrestles with God". The Bible mentions that Jacob wrestled with God.
BTW I am not a historian, I just copied a lot of this from Wikipedia.