When will Israel once again be called God's people?
Israel will once again be called God's people when they come back in complete belief, which occurs at the return of Christ. This follows the calling out of a people for His name from among the Gentiles, who are referred to as His born ones, not in the same intimate relationship.
Les explains that after Peter quieted the opposing Jews, James cited the prophets, including Amos, that after God calls out a people for His name from the Gentiles, He will build again the tabernacle of David. The conclusion was that God is calling out Gentiles for His name. However, Gentiles do not come into the intimate relationship God had with Israel when He called them 'My people.' When Israel fell away in unbelief, God said to Moses, 'Thy people.' It will not be until Israel comes back in complete belief, at the return of Christ, that they will once again be called God's people, or 'My people.' Other than this portion in Acts, Gentiles are more correctly referred to as His born ones.