(note for a Bible Study)
In Hosea 1, the prophet has two children who received the God-given names, Lo-ami (not my people) and Lo-ruhamah (no-mercy/compassion). These children will be emblems for the rejection of the Kingdom of Israel – and also tokens of hope, because God will again show mercy upon “my people”.

To rightly understand the significance of these names, we need to understand the biblical theology which underscores these names. The names have roots in the covenant and tie us to the New Testament.

“my people”

While the primary uses for Hosea come from Exodus, there uses in Genesis which help us understand the significance.

The phrase “my people” has the obvious significance of one’s own familial relations. So Ephron the Hittite uses the phrase “my people” in Genesis 23:11 to refer to his relations. It used in a similar way by Jacob in Genesis 49:29, when he speaks of death, when “I am to be gathered to my people.”

The phrase not only means relations, it also signifies dominion or kingship. So, Pharaoh in Genesis 41:40 refers to the people of the kingdom as “my people”.

God first uses the phrase “my people” when speaking to Moses from the burning bush in Exodus 3, “I have seen the affliction of my people”. Ex. 3:7. Moses is sent to Pharaoh to rescue “my people.” Ex. 3:10

When Moses comes to Pharaoh, he gives the command of the Lord, “Let my people go.” Ex. 5:1. Moses then repeatedly uses the phrase to refer to the Israelites, 7.4, 7.16, 7.26, 8.16. Indeed, one level of understanding of the conflict is a dispute between God and Pharaoh over who has dominion over Israel.

Finally, Pharaoh makes a distinction between Israel and Egypt (a distinction which God first made) when he tells Moses, “go out from among my people”. Ex. 12:31.

God then Israel out to the wilderness where he makes a covenant with them. There was also an earlier covenant with Abraham which was the (a?) basis for the designation of the descendants of Abraham as “my people”.

God then speaks to Israel and tells them that when they interact with another Israelite, they are meeting one who belongs to God, “My people”. Ex. 22:24

When God comes to establish a king over Israel, he is to protect “My people”. 1 Sam. 9:16. David is then given the task of caring for “my people”. 2 Sam. 3:18, 5:2, 7:7.

When Solomon comes to the throne, the Lord makes a covenant with Solomon, that if Solomon will keep the covenant, God will not “forsake my people”. 1 Kings 6:13 [Solomon of course fails in this respect. But a second and greater son of David will come who will be king and will keep the covenant; thus, the Lord will never forsake “my people”]

The people fail in their covenant with God, and so God addresses the fault of “my people”. Isaiah 1:3, “my people do not understand.” “My people have committed two evils”. Jer. 2:31 “My people have forgotten me.” Jer. 18:15

But there will be a restoration of “my people”. The Servant will be “stricken for the transgression of my people.” Isaiah 53:8. The “days are coming, declares the Lord, when I will restore the fortunes of my people”.

Ezekiel 37:13 (ESV)
13 And you shall know that I am the Lord, when I open your graves, and raise you from your graves, O my people.

This is the promise of Hosea, and of the other prophets, e.g., Joel 2:26-27.

As for compassion/mercy, that too is anchored in the Mosaic covenant and extends through the exile to the restoration (the Second Exodus)

In Exodus 33:19 (the first use of this particular word), God announces this compassion as his sovereign prerogative:

Exodus 33:19 (ESV)
19 And he said, “I will make all my goodness pass before you and will proclaim before you my name ‘The Lord.’ And I will be gracious to whom I will be gracious, and will show mercy on whom I will show mercy.

God speaks of compassion as a fundamental benefit of keeping his covenant. Dt. 13:18-19. In 2 Kings 13:23, God determines to show compassion upon Israel, because of his covenant.

God then says, because his people will not keep covenant, he will no longer show them compassion. Is. 9:17, 27:11. And those who bring the judgment will themselves have no compassion. Is. 13:18, Jer. 6:23, 13:14, 21:7.

But with the judgment there comes a promise of future compassion. While there will be repentance, the compassion begins in God. Jer. 31:20. Yet, the compassion will begin when they repent. Dt. 30:3, 1 Kings 8:50, Is. 30:18, 55:7; Jer. 12:15, 30:18, 31:20, 50:42; Micah 7:18; Zech. 10:6 The judgment is temporary, it is compassion which will be eternal. Is. 54:8-10; Lam. 3:32.

There are also prayers for God’s future compassion and restoration: Zech. 1:2; Ps. 103:13.

The two strands (both laid out by Hosea’s children) are brought together in the NT:
Romans 9:15–26 (NASB95)
15 For He says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.”
16 So then it does not depend on the man who wills or the man who runs, but on God who has mercy.
17 For the Scripture says to Pharaoh, “For this very purpose I raised you up, to demonstrate My power in you, and that My name might be proclaimed throughout the whole earth.”
18 So then He has mercy on whom He desires, and He hardens whom He desires.
19 You will say to me then, “Why does He still find fault? For who resists His will?”
20 On the contrary, who are you, O man, who answers back to God? The thing molded will not say to the molder, “Why did you make me like this,” will it?
21 Or does not the potter have a right over the clay, to make from the same lump one vessel for honorable use and another for common use?
22 What if God, although willing to demonstrate His wrath and to make His power known, endured with much patience vessels of wrath prepared for destruction?
23 And He did so to make known the riches of His glory upon vessels of mercy, which He prepared beforehand for glory,
24 even us, whom He also called, not from among Jews only, but also from among Gentiles.
25 As He says also in Hosea,
“I will call those who were not My people, ‘My people,’
And her who was not beloved, ‘beloved.’ ”
26 “And it shall be that in the place where it was said to them, ‘you are not My people,’
There they shall be called sons of the living God.”

1 Peter 2:9–10 (NASB95)
9 But you are a chosen race, a royal priesthood, a holy nation, a people for God’s own possession, so that you may proclaim the excellencies of Him who has called you out of darkness into His marvelous light;
10 for you once were not a people, but now you are the people of God; you had not received mercy, but now you have received mercy.