James Gatz — that was really, or at least legally, his name.
Making a Name
Not until Chapter VI, more than halfway through the novel, do we hear of Gatsby’s legal name. Indeed, before this point, we don’t even know that “Gatsby” isn’t his real name. Clearly, Gatsby makes no sincere attempts to reveal his family name, instead hiding it from society; his former, legal title appears as invisible as his servants.
Gatsby doesn’t want his name to be associated with anonymity, but instead to be as well-known as the names of famous, elite, aristocratic families. As a result, he not only literally changes his obscure family name, making himself a new one, but figuratively attempts to “make himself a name” as well.
Realistically, the name may be a reference to the Gatling gun.
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