Jordan Baker seems to keep her opinions to herself more than the others, yet she is not part of any subterfuge as is Gatsby, Tom, Myrtle and Daisy.
Honestly, I think all of the characters in "The Great Gatsby" are secretive, except for Nick. Some more than others, but each of the major characters has something to hide. Tom is secretive about his affair with Myrtle Wilson and she keeps that secret from her husband George. Gatsby is secretive about where he came by all of his money and Wolfsheim is secretive about his involvement in the underworld. Jordan is secretive about her past life and is never completely honest with Nick. I think if you look carefully at the lives of Daisy and Tom you can see that they are secretive about their marriage. Daisy leads Jay Gatsby on and makes him dream about a chance, but then she really has not intention of leaving Tom. They are all secretive about the car accident which kills Myrtle. The corruption runs deep in the whole novel and that is part of what Fitzgerald is trying to get across to the reader. He really didn't like the "money people" and continues to show us the hypocrisy of all of the characters. One of my favorite lines is when Nick tells Gatsby that he "is worth the whole lot of them."
A lot of people would argue that Gatsby is the most secretive of the bunch. I agree with the poster below that they all have their secrets to keep, but Gatsby didn't seem to keep his out of fear of anyone finding out. No one cared to get to know Gatsby--he threw great parties, everyone had a good time, and Gatsby had his focus on getting Daisy back.
Daisy, Tom, and Myrtle kept secrets in order to keep themselves from getting in trouble, or, if you want to be kind, in order to keep others from being hurt. I would argue that Daisy is the most secretive of them all. While Tom and Myrtle almost flaunt their affair, Daisy's desires and despairs and kept locked away from even Nick. Being a woman in that time period lead to suppression that wasn't expect from the men,