Be careful of the silly rhetoric of the false Jews that come here who follow the "synagogue of Satan".
The MAJORITY of the Hosea prophecy God gave through His prophet Hosea is TO THE TEN TRIBES OF THE NORTHERN "KINGDOM OF ISRAEL" or "HOUSE OF ISRAEL".
Per the 1 Kings 11 Chapter, God was angry with Solomon because he allowed his many wives to bring their idol worship in among the children of Israel. And He warned Solomon about it, but Solomon would not change. So God rent the kingdom in two, but He waited to do it in the days of Solomon's son Rehoboam.
Jeroboam of the tribe of Ephraim, was setup as a governor over the northern ten tribes by Solomon. But when Solomon heard that God's prophet Ahijah came to Jeroboam, and tore Jeroboam's new coat into 12 pieces and gave Jeroboam 10 pieces, God telling Jeroboam He would make him king over Israel (ten tribes), then Solomon sought to kill Jeroboam.
Then God split old Israel into two separate kingdoms. Rehoboam, king of Judah, of the house of David, became king over the southern "kingdom of Judah" at Jerusalem-Judea. And ONLY the tribe of Benjamin was with him there, as written in 1 Kings 12. The rest of the tribes of Israel remained in the northern holy land and made up the "kingdom of Israel", or "house of Israel" under Jeroboam, king of Israel, also written in those 1 Kings 12 forward chapters.
And because the requirement then was for all to come worship God at Jerusalem, king Jeroboam over the ten northern tribes feared that many of the ten tribes would go to Jerusalem and augment the "kingdom of Judah" under Solomon's son Rehoboam. So Jeroboam, king of Israel, setup two calf idols in false worship in the north, and made common priests of the people, and told Israel here's your gods. The Levite priests in the north, having been prevented from their priest duties, thus left the north and went to Jerusalem and sided with Judah and Benjamin. A small remnant out of the northern ten tribes also refused the calf idols and went to side with Judah. Then the two kingdoms had war against each other.
After a while, through generations of kings of both kingdoms, God finally got tired of Jeroboam's calf idol worship in the northern kingdom, so He cast the northern ten tribes out of the holy land, captive to Assyria and the lands of the Medes (2 Kings 17). They were never to return to the holy land as a people, and are still scattered to this day, and thus the name 'ten lost tribes of Israel'.
But the Genesis 48 prophecy to Ephraim was that his seed would become "a multitude of nations", and even to Jacob before that in Gen.35 that his seed would become "a company of nations". The Jews have always tried to HIDE this prophecy. They are against it, because the false Jews among them of God's enemies, those Jesus called the "synagogue of Satan", i.e., Satan's host crept in among them, are the actual ones calling the shots in the Jew's religion, and in today's Jerusalem, and even in many top positions in governments.
But just as Joseph was separated from his brethren, likewise the ten tribes were separated from the tribes of Judah, Benjamin, and Levi, even as it still is to this day. However, did Joseph fall into havoc and despair to become nothing? No! Joseph became 2nd in head of all Egypt, put in charge over making sure the people would survive the famine. Likewise with Ephraim and ten tribes, scattered to the "wilderness", like Joseph in Egypt, God blessed Ephraim and the northern ten tribes while scattered, and they became the WESTERN CHRISTIAN NATIONS of history! That FULFILLED THE "MULTITUDE OF NATIONS" THAT EPHRAIM WAS PROPHESIED TO BECOME! And of course the Jews don't like for you to hear about that! While the majority of Jews rejected Jesus of Nazareth as The Christ, The Gospel would then go to the LOST TEN TRIBES and to the Gentiles who believed which they were scattered among, becoming CHRIST'S CHURCH, initially in the Christian Western nations of Asia Minor and Europe. Britain was actually the first nation on a national scale to accept Jesus Christ as their Savior. Thus the Jews hate any reference to Britain in this prophecy also. Yet Britain was just one nation among the "multitude of nations" fulfillment. Even the United States of America is included in that "multitude of nations" alignment under Ephraim.
So the Book of Hosea is about the time when God got fed up with the calf idols of the northern ten tribe kingdom under Jeroboam, and was getting ready to scatter the ten tribes out of the holy land. THAT... is when God called them 'Lo-Ami', meaning 'not My people'. He had given them a symbolic bill of divorce and scattered them.
BUT... after He had scattered them to the "wilderness" of Hosea 2, He then said He would speak softly to them, and give them a COVENANT, and they would become Ami, meaning 'MY PEOPLE' again, and even those Gentiles who believed along with them! (per Paul in Romans 9).
Thus the false Jew liars here DO NOT WANT YOU TO READ THAT HOSEA 2 CHAPTER where God revealed a RETURN OF ACCEPTANCE OF THE TEN LOST TRIBES back into His Heart, and believing Gentiles along with them, ALL IN THE GOSPEL OF JESUS CHRIST!