Gatsby is a very cool nickname! And the story itself really gives us an apt picture of the pleasures and depravity of this world.
And yes the story itself is a very good picture on American Culture and I feel it is very representative of our culture today (though we have a little more technology). Lots of common themes in the book I see in my society today, such as the divide between rich and poor, new money vs old money, the raucous party scene, the dramas in peoples lives like affairs and betrayls, and of course the issue of Identity (Gatsby vs James Gatz) is something that is extremely common among modern American Culture.
Also the rumors concerning Gatsby are very much reflective of modern American Culture. Like how people think Gatsby was a nazi spy when in fact they never even met Gatsby. Going back to myself, my insulting nickname was Shadow (because I am extremely pale lol). This name spread like wildfire and people be talking about Shadow in our school and all the crazy stuff he do, most of which was pure mythos. I remember some of my other very good friends from the more preppy clique of kids talking about "This Shadow kid" and all the stories true and false associated with the nickname and how they didn't like Shadow even though they never met him (not realizing they were in fact talking about me to my face.) They didn't realize I was even the same person as Shadow until another friend of mine addressed me as Shadow one day in front of them. Lol, it goes without saying their surprise was quite amusing.