There are many times in God's word where he refers to his people as, "My people", but there a few specific times where God uses the phrases that we will be looking at below. As part of God's method to convey a special meaning I believe that in each instance below the same people or a segment of the same people are being addressed by the phrases "not my people" or "not a people" as when God uses the phrase, "My people". Think of it as a name. In fact in Hosea 1:9 Yahweh instructs Hosea to name one of his children Lo-ammi which means "not my people". I think it is significant. Read on and see what you think.
Deuteronomy 32:21 "They have moved me to jealousy with that which is not God; they have provoked me to anger with their vanities: and I will move them to jealousy with those which are not a people; I will provoke them to anger with a foolish nation."
Isaiah 7:8 "For the head of Syria is Damascus, and the head of Damascus is Rezin; and within threescore and five years shall Ephraim be broken, that it be not a people."
Isaiah 8:19 "And when they shall say unto you, Seek unto them that have familiar spirits, and unto wizards that peep, and that mutter: should not a people seek unto their God? for the living to the dead?"
Hosea 1:9 "Then said God, Call his name Loammi: for ye are not my people, and I will not be your God."
Hosea 1:10 "Yet the number of the children of Israel shall be as the sand of the sea, which cannot be measured nor numbered; and it shall come to pass, that in the place where it was said unto them, Ye are not my people, there it shall be said unto them, Ye are the sons of the living God."
Hosea 2:23 "And I will sow her unto me in the earth; and I will have mercy upon her that had not obtained mercy; and I will say to them which were not my people, Thou art my people; and they shall say, Thou art my God."
Romans 9:25 "As he saith also in Hosea, I will call them my people, which were not my people; and her beloved, which was not beloved."
Romans 9:26 "And it shall come to pass, that in the place where it was said unto them, Ye are not my people; there shall they be called the children of the living God."
1 Peter 2:10 "Which in time past were not a people, but are now the people of God: which had not obtained mercy, but now have obtained mercy."
Romans 9:26 repeats the prophecy of Hosea. 1 Peter 2:10 shows that the prophecy has been fulfilled.
If you want to understand the whole story read Romans chapter 9:1-24. Then in verse 25 Paul explains who are the Gentiles in verse 24. Turn back and read the first two chapters of Hosea otherwise you will be mistaken about who those "not my people" are because of what we were all taught in our churches. This prophecy is all about the ten lost tribes of the house of Israel.
For those of you who think that there was an amalgamation of the house of Israel read Amos 9:9 and James 1:1. Of course these verses are just the beginning. There is so much more spread throughout the Word. When you read the word "Gentiles" realize that the original word just means "Nation". Most of the time in the New Testament that word is referring to the children of Israel who are living among the Nations or Gentiles. You can usually tell by the context if you will carefully search and read. If you would like to read more on this may I recommend the web page Christian Israel.
"...wherefore there are but two tribes in Asia and Europe subject to the Romans, while the Ten Tribes are beyond the Euphrates till now, and are an immense multitude, and not to be estimated by numbers." Flavius Josephus, historian and contemporary of the Apostle Peter.
Romans 11:2 "God has not cast away His people whom He foreknew. Or do you not know what the Scripture says of Elijah, how he pleads with God against Israel, saying,"...
(Verse 5) "Even so then, at this present time there is a remnant according to the election of grace."