We know that the Church with the addition of the gentiles called, is Israel because God Identifies the call of the Gentiles as Israel Acts 15:16-17
16 After this I will return, and will build again the tabernacle of David, which is fallen down; and I will build again the ruins thereof, and I will set it up:
17 That the residue of men might seek after the Lord, and all the Gentiles, upon whom my name is called, saith the Lord, who doeth all these things.
Notice " and all the Gentiles" upon whom my name is called". This could be rendered:
Upon whom my name is called - Who are called by my name, or who are regarded as my people.
Now who or what People are regarded as Gods People ? Ps 81:8
Hear, O my people, and I will testify unto thee: O Israel, if thou wilt hearken unto me;
Isa 1:3
The ox knoweth his owner, and the ass his master's crib: but Israel doth not know, my people doth not consider.
Jer 7:12
But go ye now unto my place which was in Shiloh, where I set my name at the first, and see what I did to it for the wickedness of my people Israel.
Jer 23:12
And I have seen folly in the prophets of Samaria; they prophesied in Baal, and caused my people Israel to err.
Who was the Prophet referring to here as Gods People
2 Chron 7:14
If my people, which are called by my name, shall humble themselves, and pray, and seek my face, and turn from their wicked ways; then will I hear from heaven, and will forgive their sin, and will heal their land.
Is not this a reference to Israel? And so Israel and the Name of God are synonymous.
Jesus who is God is referred to as Israel in this prophecy Isa 49:3
3 And said unto me, Thou art my servant, O Israel, in whom I will be glorified.
So the calling of the gentiles as Gods People Rom 9:25
As he saith also in Osee, I will call them my people, which were not my people; and her beloved, which was not beloved.
Paul writing to the gentile church in Corinth wrote of them as believers 2 Cor 6:16
And what agreement hath the temple of God with idols? for ye are the temple of the living God; as God hath said, I will dwell in them, and walk in them; and I will be their God, and they shall be my people.
So the Gentile Church is part of Israel, Gods chosen People, Called by His Name ! 14