The most widely held view among commentators is that the woman of Hosea 3:1 is Gomer. David Allan Hubbard (TOTC) remarks:
Any other reading would break the analogy which carries the basic
message of this section: the Lord of Israel will judge his idolatrous
people and afterwards renew his relationship with them. To introduce a
second woman would derail the entire train of thought and make wreck
of the hope which the prophet would convey to Israel.
This argument from the basic message of Hosea is a strong one.
However, if the woman of Hosea 3:1 was the same as mentioned earlier, one might expect the definite article, or for Gomer to be named again, not an anarthrous אִשָּׁה (a woman).
I don't think the identity of the anarthrous אִשָּׁה in 3:1 can be decided by the placement of "again".
Douglas Stuart (Word Commentary) argues the minority view, that the woman of Hosea 3:1 is not Gomer but a second wife. This would more naturally explain the anarthrous אִשָּׁה but introduces problems (at least superficially) for understanding the basic message of Hosea.
Stuart draws attention to the distinction between אֵ֤שֶׁת זְנוּנִים֙ in 1:2 and מְנָאָ֑פֶת in 3:1.
He explains that in 1:2 זְנוּנִים֙ (prostitutions) is an abstract noun, built on the plural pattern frequently used for abstracts as an alternative to the feminine singular. Douglas argues that this refers more to a character trait than to a profession. He states:
That she is called metaphorically an אֵ֤שֶׁת זְנוּנִים֙ “prostituting
woman” in 1:2 cannot be taken as a literal statement of her profession
or practice. She is merely an Israelite—all of whom are “prostitutes”
as the verse implies, that is, all of whom have broken Yahweh’s
In contrast, the woman Hosea marries in 3:1 is called a מְנָאָ֑פֶת, an “actual adulteress” He remarks:
His command to her concerning “prostitution” (v3) suggests that she
was indeed a professional prostitute. Hosea is no longer using זנה
metaphorically as was the case in chaps. 1 and 2.
Regarding his understanding of the message of chapters 1-3, he states:
Some interpreters have suggested that Hosea is buying back Gomer. In
2:21–22 [19–20], however, Yahweh does not buy back the same old
Israel, but a new Israel, a remnant transformed eschatologically, an
Israel he had not yet married, as it were. To assume that Gomer left
and that he then bought her back from her father or someone she had
married or a house of prostitution, still in her defiant adulterous
state (3:1), hardly comports with the picture given in 2:18–25
Thus according to Stuart, the woman of 3:1 is not Gomer, but is still symbolic of God's covenant people.