Was Gomer the same wife of Hosea mentioned in Hosea 3 or did Hosea take another wife?
Also is Romans 9:25 quoting Hosea 2:23?
To keep what happens in Hosea clear, we have to follow both the story of Hosea and the illustration God makes using Hosea's life.
"When the LORD began to speak by Hosea, the LORD said to Hosea: "Go, take yourself a wife of harlotry and children of harlotry, for the land has committed great harlotry by departing from the LORD"" (Hosea 1:2).
God tells Hosea to marry a prostitute because this is the way Israel has been treating God. Israel is in a covenant relationship with God, yet their entire history involves them worshiping idols. Hosea's marriage is going to be rough because it will be hard for a prostitute to give up her past ways. Notice that Hosea is to offer a prostitute a way out of harlotry, but she did not seek Hosea. She has no motive to make a radical break from the past beyond the gift Hosea is offering her. This is the same as Israel. God offers a covenant to Israel that they didn't ask for or desire. There should be a motive from gratefulness to be faithful to God, but it wasn't enough for Israel.
The woman Hosea married was Gomer (Hosea 1:3). They had a son name Jezreel, after the valley of Jezreel, Israel's bread basket. God declared that Israel's army would be broken there (Hosea 1:5). It was a vineyard in Jezreel that Ahab coveted that lead to his death. His son Joram died in Jezreel (II Kings 9:15). Ahab's wife died in Jezreel (I Kings 21:23; II Kings 9:30-33). The rest of Ahab's seventy sons were killed and their heads sent to Jezreel (II Kings 10:6-7). "So Jehu killed all who remained of the house of Ahab in Jezreel, and all his great men and his close acquaintances and his priests, until he left him none remaining" (II Kings 10:11). God is saying that Jehu had gone too far and that the slaughter he caused would be avenged with the destruction and captivity of Israel by the Assyrians.
The daughter was Lo-ruhamh, meaning "not having obtained mercy." God declared that the northern Kingdom of Israel had done nothing to have mercy from God and would not receive it (Hosea 1:6-7).
The third child was named Lo-ammi, meaning "not my people." God is going to reject Israel as his people, but not permanently (Hosea 1:9-10).
In the future, in Jezreel, God would again call Israel his people and give them mercy -- the reversal of the three children's names (Hosea 1:11-2:1).
But in the meantime, God is divorcing Israel for her harlotries (Hosea 2:2). Though it is not said here, it can be assumed that Hosea's wife had committed adultery and he divorced her, just as God divorced Israel. In other words Hosea is representing God and Gomer is representing Israel. There is some implications that the second and third children where not Hosea's. "I will not have mercy on her children, for they are the children of harlotry. For their mother has played the harlot; she who conceived them has behaved shamefully. For she said, 'I will go after my lovers, who give me my bread and my water, my wool and my linen, my oil and my drink'" (Hosea 2:4-5). Israel (Gomer) thought she did not need God (Hosea) and that she could survive on her own. God prevented Israel from succeeding. "She will chase her lovers, but not overtake them; yes, she will seek them, but not find them. Then she will say, 'I will go and return to my first husband, for then it was better for me than now'" (Hosea 2:7). But God (Hosea) will refuse to support her until she truly realizes how much she needs God (her husband) (Hoses 2:8-13).
But this isn't the end. God plans to lure Israel back to him. Once she realizes how much she needs God she will be truly committed to Him (Hoses 2:14-23). Notice in Hosea 2:22-23 the names of the three children are given again.
"As He says also in Hosea: "I will call them My people, who were not My people, and her beloved, who was not beloved"" (Romans 9:25) is a quote of "Then I will sow her for Myself in the earth, And I will have mercy on her who had not obtained mercy; Then I will say to those who were not My people, 'You are My people!' And they shall say, 'You are my God!'" (Hosea 2:23). It is not a word-for-word quote. It keeps the sense of what Hosea recorded but rewords it to fit better with how Paul was making his argument. In today's terminology it would be called a dynamic equivalent translation of the original Hebrew. Paul inverted two clauses to put more emphasis on the saving of the Gentiles.
The next verse in Romans, "And it shall come to pass in the place where it was said to them, 'You are not My people,' There they shall be called sons of the living God" (Romans 9:26) is based on "Yet the number of the children of Israel Shall be as the sand of the sea, Which cannot be measured or numbered. And it shall come to pass In the place where it was said to them, 'You are not My people,' There it shall be said to them, 'You are sons of the living God'" (Hosea 1:10).
We return to the story of Hosea in chapter 3. "Then the LORD said to me, "Go again, love a woman who is loved by a lover and is committing adultery, just like the love of the LORD for the children of Israel, who look to other gods and love the raisin cakes of the pagans"" (Hosea 3:1). This is still the story of God restoring Israel to Himself. So the woman is Gomer. She is no longer deserving to be called Hosea's wife, but Hosea is to show love for this woman, just as God continues to show love for faithless Israel.
We can surmise that Gomer thought she could go back to prostitution and support herself. But it didn't work. She was sold off into slavery for her debts, and Hosea had to buy her back (Hosea 3:2). Hosea insisted that there would be a trial period before he would accept her back into his bed. "And I said to her, "You shall stay with me many days; you shall not play the harlot, nor shall you have a man - so, too, will I be toward you"" (Hosea 3:3). This represented the period of time Israel went without a king (Hosea 3:4). But afterwards, they would turn back to God (Hosea 3:5). By this, after the long wait, Gomer would give her full heart to her husband who did so much to save her from herself.
The parallels work between God's dealing with Israel and Hosea's dealings with Gomer. When God rejected Israel and sent them off into captivity under Assyria, He did not find a new nation to enter into His covenant. He restored Israel after the Babylonian captivity. For this reason we can assert that it is Gomer that Hosea brought back in Hosea 3.