The wisdom of the original way that the Book of Mormon Isaiah chapters were divided over the Biblical model is evident here. This verse is part of the calamity of the last chapter, and in the next verse the emphasis will shift to the beginning of the redemption of the righteous.
At this point, however, there is still an emphasis on the destruction. At the end of the last chapter it noted that the men would fall in war. That leads directly to the problem of the women in this verse. A woman’s place in society at that time was dependent upon her position within a patriarchal family. With so many women who no longer have husbands or fathers, many would want to improve their situation by becoming attached to any man.
The point of this verse is to show their desperation. They need the man’s name to remove their social reproach, and are willing to accept that name without the accompanying support that is typically associated with the family.