The Old Covenant of Law only started for Israel at Exodus 24. Israel the nation needed to acknowledge that they would obey the conditions stipulated in that covenant.
7 And he took the book of the covenant, and read in the audience of the people: and they said, All that the Lord hath said will we do, and be obedient.
8 And Moses took the blood, and sprinkled it on the people, and said, Behold the blood of the covenant, which the Lord hath made with you concerning all these words.
So for the New Covenant, as stated clearly in Hebrews 8, the entire nation of Israel will similarly have to acknowledge the conditions stipulated in the New Covenant, that is to believe Jesus is the Christ, the promised Son of God (John 20:31), before that New Covenant could begin for them.
As far as Acts tells us, the nation's leaders, the Sanhedrin, prefer to stone Stephen, so they have rejected Christ. So currently, the New Covenant has not begun for the House of Israel.
And no, we in the Body of Christ do not get the opportunity to insert ourselves into Hebrews 8:8, and call ourselves Israel, in order to accept the New Covenant on their behalf.