Answer:
Yes, Nathaniel Hawthorne was right in naming Brown's wife "Faith".
Faith is a representation of the faith and belief of not only Brown himself but also that of the believers/ Christians who are tempted everyday by the devil. In her attempts to persuade Brown to not go into the forest, telling him about the dream, she is the 'spiritual' image of God who is trying to stop his people from being cheated/ tempted or brought to sin.
Brown initially has full faith in his wife but at the end of the story, we see him a changed man. He no longer sees her as the woman she was in the start but he began to question her each and every actions.
Explanation:
Nathaniel Hawthorne's "Young Goodman Brown" tells the complex tale of the character Young Goodman Brown and his conflicting belief in his own faith and later on, that of his villagers including his own wife. He had left his village and his wife to be tempted by the devil, returning back a shaken man altogether.
Hawthorne had aptly named "Faith", the wife of Goodman Brown for she represents the faith and innocence of the true Puritan believer. She is the epitome of what a believer of God should be but she appears in a different light in her husband's face after his return from the forest. From her reluctance to let Brown go into the forest to be tempted by the devil, she represents a Christian's life to stay away from any devilish temptation. She is the 'spiritual' representation of God trying to prevent His people from being tempted.
At first, Brown seems to have full faith in her naivety and innocence. He even expresses regret in leaving her all alone to be tempted in the forest. But after the devil had tempted him and had taken him through the evil ceremony of inducting the 'new converts' to the devil, he began to question her character and could not seem to see her in the same position he had put her before the temptation. There is no proof that what happened in the forest was real, but what the devil intended to d has had its effect. Brown now no longer trusts her, nor the village priest and others. he began to question each an everyone's faith, ever doubting them.