Gatsby worked hard to present the impression that he was "old money" for a number of reasons.
He was distancing himself from the reality of his actual background. "His parents were shiftless and unsuccessful farm people" - certainly not acceptable for the vision Gatsby wanted to build for himself as his life story.
Gatsby wanted to impress Daisy and her family, and they legitimately were old money. When he first discovered and fell in love with her, Daisy was still a teen-aged beauty living with her parents in their Louisville mansion with "the largest of the lawns."
The social scene and the most exciting elements of the business scene, the parts of the business world that Gatsby became involved with, all subscribed to the idea that material wealth and elaborate displays of all that it could buy were signs of being successful and accepted, which Gatsby wanted most of all. The excessive parties, the extent of his wardrobe, and all the rest of the props he used to decorate himself and his life - all were intended to impress others and to reinforce the fiction that he wanted to believe was his reality.
Through out the story, Jay Gatsby tries to convey an image of a person to be respected. To be born into a world of privillage, especially in the era when the story takes place, is a very clear sign of a person that is often respected by the people that Gatsby wanted to impress. And also, keep in mind the background of Gatsby. How would he envision a person of "old money"? He would probably think highly of, and try to emulate a person of multi-generational wealth. To him, this person would embody glamor and class. In the current era, a person might have the same opinion of a super-model or a blockbuster moviestar. I hope this helps!