How do the rumors about Gatsby affect his image and reputation?

When Nick finally attends his first party at Gatsby's palatial home, he finds that rumors about his neighbor abound.
Two of the girls at the party who know Jordan Baker say that Gatsby killed a man, after which news Nick records that

A thrill passed over all of us.

Another person at the party states that Gatsby was a German spy during World War I, while someone else insists he was in the American army. Jordan later offers a rumor, which she says she doesn't believe, that Gatsby attended Oxford.
In chapter four, Nick hears that Gatsby is a bootlegger and a nephew of von Hindenburg. Because the rumors are so varied and so wild, we really have no reliable way of knowing how Gatsby got his fortune and how he is able to throw his lavish, wild parties.
The rumors about Gatsby therefore add a sense of mystery to him and make him seem a figure larger than life.
As Nick notes of Gatsby:

It was testimony to the romantic speculation he inspired that there were whispers about him . . .

Not knowing the facts about him adds to his mystique and aura. He seems to have walked off the pages of a romance novel.