In a description of the Youngs' cheap apartment, the story uses personification of the name-card on the mailbox to reflect the couple's fluctuating fortunes. The letters of Jim's middle name, Dillingham, are depicted as if they're human:
The 'Dillingham' had been flung to the breeze during a former period of prosperity when its possessor was being paid $30 per week. Now, when the income was shrunk to $20, the letters of 'Dillingham' looked blurred, as though they were thinking seriously of contracting to a modest and unassuming.
When Jim's weekly income shrinks significantly, the "Dillingham" looks like it wants to shrink in proportion to the family's reduced circumstances. Obviously, letters on a mailbox do not have a mind of their own. But by portraying the letters as if they're "thinking seriously of contracting" to a modest single initial, the author hints at the Youngs' own feelings about Jim's lower wages. Now that Jim is earning less money, in other words, he and Della no longer feel entitled to flaunt Jim's fancy middle name; they feel it's more suitable to stick to a name that appears "unassuming," befitting someone who earns a mere $20 per week. This is meant to be somewhat humorous: "Dillingham" is part of Jim's name no matter how much money he earns, so there's no reason he shouldn't put it on the letter-box if he chooses.
But the personification of the letters shows that, for a young family struggling to get by, small details take on a dramatic importance. In a setting where people are very aware of one another's social standing, it's easy to worry about others' perceptions (that is, others might think the Youngs are pretentious or putting on airs by displaying "Dillingham"). The gentle humor also fits with the author's overall tone. O. Henry has a positive attitude toward the characters, but he also hints that, in the greater scheme of things, the details that feel incredibly important to this young couple aren't really worth fretting about.