The narrator really doesn't beat around the bush with this one. We get a bunch of paragraphs that start with a sentence that basically says, "Ok, I'm the narrator and I'm the boss, and I'm going to go ahead and tell you all about this particular person. For example, in the intro to Kovalev, the narrator busts out with "Here let me add something which may enable the reader to perceive just what the Collegiate Assessor was like" (2.2).
It's a straightforward deal—he tells us, we listen, and we believe him.
Everything we want to know about the relationship between Kovalev and his newly independent nose can be explained by their relative positions on the social ladder. We already know that Kovalev is a striver, whose main goal in life is to climb higher in the ranks and to demand respect from everyone beneath him. A man like that is totally freaked out by his superiors—which is exactly what the nose becomes.
Once he sees the thing dressed like a State Councilor, Kovalev is so stressed that he can't even bring himself to speak to it, let alone demand that it get back onto his face. The only time he gets enough courage to yell at it is when the cop brings it back to his house stripped of all the fancy titles and ranks. Way to kick a nose when it's down, Kovalev.
Clothes get a lot of play in the story. We get some detailed descriptions of what the barber wears, what the nose wears, what the ladies Kovalev wants to flirt with but can't are wearing, and so on. Why?
Well, clothes were a really big deal in the 19th century, in the days when they were probably the most expensive thing anyone owned because they were hand sewn to fit by a tailor. Back then clothes were a pretty useful external marker of social and economic status, of living habits, and just a good way to size people up in the street. Gee, it's a good thing that we've all matured since then. Right?