During the era of the 1920s, the setting of The Great Gatsby, a time not too distant from those years which saw many a European immigrant enter New York harbor, many people's nationalities were distinguishable by their coloring and facial appearances, and especially the shape of their noses. Greeks and Italian immigrants, for instance, were olive-skinned and had longer aquiline noses, generally speaking. Jewish people, especially those who were Semites, had a distinctive nose. And many jokes were made about the "lack of a nose," small pug noses of the Celtic people such as the Irish, Welsh, and some Scots. In the Eastern states, there was a certain snobbery among those with names such as Henry Cabot Lodge, Astor, Vanderbuilt and so on. These WASPs (White Anglo-Saxon Protestants) were the ruling social class.
When Nick Carraway (like F. Scott Fitzgerald himself) moves to the East from the Midwest, he notices this upper class/"blue-blood" snobbery that is exemplified in Chapter 6 in which Gatsby is only ostensibly invited for the sake of appearances by the upper class Mrs. Sloane to horseback ride with them and offers to catch up with them in his car.
"My God, I believe the man's coming" said Tom. "Doesn't he know she doesn't want him?"
Ironically, Tom Buchanan (whose name is Scottish, not English like the Sloanes and others in East Egg) is a poser himself, as is Gatsby, who has changed his name to sound English. This assumption of upper-class status explains why Tom is really a brawler and not a gentleman. His hiring of the former silver polisher from another family as his butler demonstrates his lack of class sense, as well. (The butler has had to leave his position as silver polisher because he is allergic to the chemicals in the polish.) Symbolically, then, the butler's nose is placed above his usual station in that he has a position higher than his person rates; he would have been a footman in the other household, but is moved up to being a butler in the Buchanan's household--symbolically an upstart and poser like Tom Buchanan.
Interestingly, when Myrtle Wilson feigns that she is wealthy, wearing a lovely dress given her by Tom at the New York apartment, she screams Daisy's name and Tom breaks her nose as she, a poor woman, assumes that she can retaliate against Daisy. The nose break reminds the reader of Myrtle's having been put back into her social place after, as the old expression goes, having had her "nose out of joint." Now, it literally is that way.
Meyer Wolfschiem (with this name, for some reason, Fitzgerald inverts the usual German placement of the -ei- in names with -heim at the end) suggests the Jewish Mafia leader, Meyer Lanksy, known as the "Mob's Accountant" who was closely associated with Lucky Luciano--two very dangerous mobsters of the Twenties.
That Dr. Eckleburg has no nose perhaps indicates the intention of making his face universal and not limited to any nationality or race. For, as Wilson's believes, he is perceived as God looking down upon the material waste generated by man and seeing beyond the Valley of Ashes into the empty souls of the "Lost Generation." "God sees everything," remarks the tragic George Wilson whose dream of leaving his poor situation in the Valley literally ends in ashes as he and Myrtle die:
"Ashes to ashes, dust to dust", a phrase from the Anglican Book of Common Prayer burial service.
So, while "a rose is a rose" as Juliet says, in The Great Gatsby, a nose is not just a nose.