I believe 'Jerusalem' is a Hebrew word meaning 'city of peace'. Pre-Israel it was called Jebus (home of the Jebusites). The whole Israel thing is quite strange. The terms 'Jew' and 'Semite' are not easy to define and Israel is the god given name of Jacob by whom the Israelites are defined. Yet many Israelis would find it pretty hard to prove their lineage from Jacob.

To be a Jew you only need to convert to the Jewish faith, much like to be a Christian you need to profess your loyalty to Jesus. There is no 'Christian' culture but there are Christian communities and similarly there are Muslim and Jewish communities with histories going back centuries. However justifying the modern state of Israel by appealing to history is like painting a landscape in watercolours in the rain.