The title of this story seems pretty straightforward, right? It is a diary, and it is written by a madman. What more could there be to that? Well, hold on a second, though.
Let's think about what would it would be like if it were called something else. Say it were called "A Diary." We would start reading it, and sure, it would look like a diary with all these entries. But when we got to the part about the dogs talking, we would get very confused, right? We could even think it was magical realism. Especially since that's one of the tricks usually up Gogol's nose, er, sleeve. So by calling this one "A Madman's Diary," instead of just "A Diary," Gogol is making sure we don't toss the story aside or confuse it with magical realism when we get to the nuttier parts.
Let's think of another title. What if it were called "The Titular Councillor" or even "The King of Spain"? Would those seem more or less exciting to you than "The Diary of a Madman," with all its promise of insanity? We think the original title wins.