As the book opens Jay Gatsby is in the process of self-reinvention. He has made a great deal of money in a criminal trade, a business never actually identified but presumed to be bootlegging. He downplays his criminal past and plays up his great wealth to win back Daisy Buchanan, a girl who had rejected him years earlier because of his poverty.
Gatsby embodies much of what we Americans admire. He has succeeded in his business, made himself extremely wealthy, yearns for a rise in social status, and hasn't forgotten an early love. He ticks all the boxes. So, even though he's a criminal who's using his ill-gotten money to steal another man's wife, we tend to like him and are saddened by his death. Victimless crime is not something we particularly hold against him. Gatsby is not just self-made, but also self-remade, and we admire him for that.
American history is filled with men (and they are usually men) who can be called "Gatsby-like" or "Gatsbyesque." They've made money in some unsavory business and they want to hide that fact in order to be accepted by respectable society. Sometimes they've gone straight, while sometimes-like Gatsby-they haven't entirely left the old life behind. But they've learned to compartmentalize and want to be acknowledged as something they're not. The Gilded Age-the decades before and just after the turn of the last century-was filled with self-made businessmen who hoped people would forget their ruthless business practices and remember their charitable work and their lavish lifestyles. Carnegie, Rockefeller, Vanderbilt-the Robber Barons became the American aristocracy.
Scott Fitzgerald was probably thinking of all of them as he incubated Gatsby and its title character in 1923 and 1924. The Robber Barons weren't necessarily criminal but they were willing to stretch the bounds of ethics to make their millions, but they each hoped that their sumptuous homes and their generous gifts to worthy causes would mask the origins of their money. But Fitzgerald also had in mind a character whose scale was somewhere below baronial level, a man who could not just downplay but completely obscure the origin of his money.