Jay Gatsby and Don Quijote are both the result partially successful self-rebranding exercises. While Gatz was Gatsby's discarded identity, Quijote's possible former surnames include Quesada, Quijano or even Quijada.
Both characters have repositioned themselves in order to seek truth through fantasy, though Quijote is as concerned with the means as the ends; Gatsby's feelings about his own means are one of the great mysteries of Fitzgerald's novel.
I am perhaps fortunate to have two individuals in my close acquaintance that merit correlation with these great figures from literature. The first aspires to be Gatsby, but the Jay Gatsby of the means not the ends - a would-be arriviste whose state of perpetual arrival has over time led him further and further from his desired destination. His head contains ideas of fame and fortune that are far less sublimated than those that drove our aforementioned heroes. El Quijote aspires to be famoso in the old-fashioned sense of the word. Gatsby seeks symmetry in his desire for a woman whose "voice is full of money".
The other person I have in mind is more the model of the ascendant parvenu, even down to the "old sport" sort of linguistic affections. Yet he lacks Gatsby's willingness to move amongst the gregarious and you would be hard-pressed to identify his little green light. Instead he has the Quixotic tendency to hold a mirror up to himself in everything he does, as if deep-down he has concluded that embodying the paradigm will be sufficient reward in this life.