What difference does Nick imply between "really" and "legally" when he says that James Gatz was "really, or at least legally" Gatsby's name?

When they reached the door of the lonely house and stopped to unlock it, and the cat came to purr loudly, and rub against them, a deserted p***y, indeed, but fat with young robins, sylvia whispered that this was a beautiful place to live in, and she never should wish to go home. the description of the house in this excerpt gives an example of