The text states specifically that "they carved no hopeful verse upon his tombstone, for his dying hour was gloom." No doubt the tombstone had his name on it along with the year of his birth and death. Since eNotes allows for answering only two questions per posting, I will answer the next one in order, which is: "Where is Young Goodman Brown headed after sunset?" He has an engagement to attend an initiation ceremony held by a host of devil worshippers, including the town's most respected citizens, deep in the forest. The author does not explain how he came to be invited. It almost seems that this is something expected of every young man and woman when they reach a certain age. There is some resemblance in this respect to Shirley Jackson's "The Lottery."
The depressing last lines of Nathaniel Hawthorne's "Young Goodman Brown" (1835) reveal that the titular character's grave held no "hopeful verse": "they carved no hopeful verse upon his tombstone, for his dying hour was gloom." This "hopeful verse" is most likely a Bible verse, given the story's Puritan frame. Why, however, did Hawthorne add this ostensibly trivial detail?
In this short tale, Young Goodman Brown, a newly married gentleman from Salem village, leaves his wife Faith one night and goes into the nearby woods. He encounters some of the fellow townsfolk committing acts of devil-worship and thinks he hears the voice of his wife. When Young Goodman Brown returns to Salem, he is trembling, uncertain of whether what he saw in the forest was real or a dream, and the rest of his days are somber and bleak.
What are we to make of this? Given the connection between Salem village and the infamous Salem Witch Trials, and the Devil's reference to Young Goodman Brown's father burning Native American villages, the story seems to be about human moral hypocrisy. Just as the characters in the story worship God by day but the devil by night, the early Puritans committed atrocious crimes in the name of religion. "Young Goodman Brown" then establishes the dual capacity of the human heart to simultaneously act in good and evil ways.
How does this relate to the unmarked grave then? Those who buried Young Goodman Brown didn't care to add a hopeful Christian message to his grave. With this, Hawthorne suggests that humanity, due to our dual nature, isn't worthy of a hopeful verse as well. A bit heavy, huh?