In that day I will raise up the fallen tabernacle of David and I will wall up its breaches and raise up its ruins and build it up as it was in the days of old; that they may possess the remnant of Edom and all the nations which are called by My name, declares Jehovah who does this. Amos 9:1-12

In Amos, God came in to promise that some day He would come back to restore the fallen kingdom of David.  In that day the kingdom of David and the family of David will be restored  and all the nations will be called by the name of Jehovah.

When Christ comes back, in His last appearing, He will be the real David to restore His kingdom and His royal family.  That will be the millennial kingdom, in which all the nations will be called by the name of Jehovah, that is, all the nations will belong to God. It was based on this that in Acts 15 James told the Jewish believers not to be bothered by Peter's and Paul's going to the Gentiles, because in the restoration all the Gentiles will belong to God, just like the Jews.

Exerpts from HWMR- Minor Prophets, Volume Two, Week 7-Day 3