Israel (Hebrew Yisrael) is one specific person in Bible history
He is the son of Isaac and Rebekah. Named Jacob ("heel catcher") at birth because of his peculiar grip on his twin brother's heel, Jacob later received a new name from the Almighty. After wrestling with the angel of God and prevailing, Jacob was named Israel. The name Israel means one who is a "prince with God" or who "has power with God."
Israel is a geographic location.
It is the name of the Canaanite land that God promised to Abraham's descendants (Genesis 12:7). This land was inhabited by the children of Israel before and after their stay in Egypt.
Israel is a group of people descended from Jacob's 12 sons.
In the ninth century B.C. there was a division between Israel's ten northern tribes and the two southern tribes. The ten northern tribes retained the name Israel, while the two southern tribes were called Judah.
At the time the Jewish people were conquered and carried off into exile, the name most properly used to describe their entire land was Israel. When the exiles returned and the land became a province of Persia, the area was more commonly known as Judea.
When Alexander the Great defeated the Persians, he attempted to Hellenize the people of Israel. In order to deny their Hebrew heritage, the Greek maps called the land Philistia after its early Philistine inhabitants (who were also referred to as Long Dead People). During this period, however, the Jewish people once again called themselves and their land Israel.
By the time of Jesus, the Jews who remained in the Diaspora (had not returned from exile) were called Israelites. Those who lived in the land called it Judea.
For political reasons, however, the Romans followed the lead of the Greeks and continued to call the land Philistia. Later Philistia was rendered Palestina in Latin, then Palestine in English.
In his writings the Apostle Paul makes reference to the Israel of God. Some church people feel that this is a reference to the larger Church, the Body of Christ. Nevertheless, most Jewish believers in Jesus think that Paul was referring to Jews who had come to faith in the Messiah.
The point that must be made is that Israel or Yisrael has always been the name of the people who are descended from Jacob, and it is also the name of the place that God gave those people since the mass return of the Exodus.