Genesis 35:10
God said to him: Your name is Jacob. You will no longer be named Jacob, but Israel will be your name. So he was named Israel.
But the Bible after that still calls him Jacob, why?
It is because Israel is the name for GOD's BIRTHRIGHT.
Not only did the Israelites have family birthrights to their eldest sons, but God also started His Birthright to the children of Israel beginning with Abraham, from which the 'seed' of Israel would be born.
This is also one of the reasons why God is called The God of Abraham, The God of Isaac, and The God of Jacob. It is about God's Promises that He first gave to Abraham, and that passed on-wards. Per 1 Chronicles 5, that Birthright finally wound upon the sons of Joseph, i.e., Ephraim and Manasseh.
The name Israel is actually the Salvation name in Christ Jesus. It means to prevail with God's help. The Angel gave Jacob the new name Israel to show The Gospel and God's promises that go with that Gospel. Christ's Church is actually a continuation of that Birthright with The Gospel. It is NOT about the old covenant. It is about the New Covenant Jesus Christ, as the Gospel Promise by Faith was given to Abraham first, 430 years prior to the law and old covenant given through Moses.
Even Melchizedek meeting Abraham and offering him "bread and wine" represents Jesus appearing to Abraham in Old Testament times and preaching The Gospel to Abraham, even before Jesus was born of woman to die on the cross...
Gal 3:6-9
6 Even as Abraham believed God, and it was accounted to him for righteousness.
7 Know ye therefore that they which are of faith, the same are the children of Abraham.
8 And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, 'In thee shall all nations be blessed.'
9 So then they which be of faith are blessed with faithful Abraham.
KJV
At the end of John 8, Lord Jesus said Abraham rejoined to see His day, and was glad. Thus the Old Testament patriarchs knew about The Gospel of Jesus Christ, and that is how the name Israel links to Christ's Church, because of The Gospel and God's Birthright blessings that go with it.
Gal 3:26-29
26 For ye are all the children of God by faith in Christ Jesus.
27 For as many of you as have been baptized into Christ have put on Christ.
28 There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus.
29 And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise.
KJV
Did you catch that last verse about believers on Christ Jesus being
heirs with Abraham according to the promise?
Thus Christ's Church = God's Israel, and visa versa.
Of course the orthodox unbelieving Jews don't like this idea by Apostle Paul, but too bad, for it is written. It's actually the unbelievers that try to hijack the title of Israel when it actually belongs to those in Christ Jesus and His Kingdom.