How do the children’s names lead from judgment to the closing promise?

The word of the Lord comes to Osee, Beeri's son, in the days of Juda's kings Ozias, Joathan, Achaz and Ezechias and Israel's king Jeroboam, son of Joas. The Lord tells him to take a wife of fornications and have children of fornications, because the land will depart from the Lord through fornication. The edition explains that the wife has been given to fornication and represents God's dealings with offending Israel; the children's designation comes from their mother's character, perhaps also their own wicked dispositions.

Osee takes Gomer, Debelaim's daughter, and she bears him a son. The Lord commands the name Jezrahel: in a little while he will visit Jezrahel's blood upon Jehu's house, end the kingdom of Israel's house and break Israel's bow in Jezrahel's valley. Gomer next bears a daughter called Without mercy, explained in the note as Lo-Ruhamah. The Lord says he will no longer add mercy to Israel but utterly forget them, while saving Juda by the Lord their God rather than bow, sword, battle, horses or horsemen. After the daughter is weaned, Gomer bears a son called Not my people, or Lo-ammi: they are not his people, and he will not be theirs.

The closing promise says Israel's children will be innumerable as sea sand. Where they were called not his people, they will be called sons of the living God. Juda and Israel will gather, appoint one head and come up out of the land; great is Jezrahel's day. The edition identifies the true Israelites with the Church of Christ's children, the one head with Christ and Jezrahel with the seed of God. The chapter does not narrate the particular killings at Jezrahel, identify Gomer's third child as her final child or give additional marriage customs.