Why did James Gatz invent Jay Gatsby?

Nick begins the story of Gatsby's past by saying that Gatsby "sprang from his Platonic conception of himself," which refers to that his ideal form. That is, the Platonic form of an object is the perfect form of that object. Therefore, Nick is suggesting that Gatsby has modeled himself on an idealized version of "Jay Gatsby": he is striving to be the man he envisions in his fondest dreams of himself. Gatsby is thus the novel's representative of the American Dream, and the story of his youth borrows on one of that dream's oldest myths: that of the self-made man. In changing his name from James Gatz to Jay Gatsby, he attempts to remake himself on his own terms; Gatsby wishes to be reborn as the aristocrat he feels himself to be.