Sometimes titles are a little mysterious, trying to push readers into finding that one reference somewhere in the text that explains just what the author meant, or doing some independent research to figure out what ancient bit of wisdom the title is referring to.
Not here. You don't have to read far to figure out that "The Nose" is named after the single most memorable thing in the story. Actually, though, the title is so no-nonsense, and even maybe a little boring, that it's like a deadpan joke for how crazy the story about the nose will actually end up being.
Oh, and for what it's worth? The word "nose" in Russian is "nos" (нос), while the word for "dream" is "son" (сон). So maybe there's a little bit of wordplay going on there as well.