Perhaps because they differ greatly from the rest of the book, the sections of Hosea which tell of his personal family life seem to be better known than the poetic passages. The relevant texts are Hosea 1 (particularly Hosea 1:2-3), and Hosea 3.
When we look at those texts, we’re immediately presented with the question of whether the two texts refer to the same woman. We are given a name in the first chapter, but not in the third, and it is easily conceivable the narratives tell of two different women. After all, it seems that God’s command to Hosea in 3:1 initiates a new action on the part of Hosea. The use of “again” (עןד) in 3:1 seems most naturally to modify “The Lord spoke to me” (so NRSV), although it could conceivably modify “go” (ESV), or even “love” (NIV—this reading seems unlikely to me, and indeed the translation of the whole verse in the NIV seems to sidestep the legitimate ambiguity.) I read the first part of the verse as saying, “The Lord said to me again, ‘Go, love a woman who has a lover and commits adultery…'”
Although that reading may suggest that Hosea is being told to love a completely new woman, I think that on the whole the analogy depends on this being the same woman from chapter one. Just as the Lord is loving Israel despite her infidelity, I think Hosea is being told to love his wife even though she has been unfaithful to him. the analogy doesn’t make sense if Hosea is starting a new relationship—that certainly isn’t what God is proclaiming he is going to do! So we’re on perhaps difficult methodological ground here. Although the intent of the passage was to make clear the Lord’s action by way of Hosea’s action, for us we almost need to reverse engineer the metaphor and interpret the reality of Hosea’s action by what it is said to have represented in the Lord’s actions. Thus, I felt comfortable letting my sermon on Hosea and Gomer grow out of this verse, because on the whole I think the data bests suggests that Gomer, the daughter of Diblaim mentioned in chapter 1, is the same person being referred to here in Chapter 3.