Maria, In the convo thread between you and the customer you'll get a "you created a private listing" notification.
Sam, You can create a private listing from convos you have with others. I'm fairly certain the option is there if THEY initiate the convo. The option to do so is located on the upper right hand corner within the convo message. I just used this option for the first time and it's pretty neat. I love that you don't get charged the listing fee until the customer has purchased the listing, and you can track the progress of the order right through there ( I wonder if the customer can too), and you're pretty much guaranteed that no one else will accidentally purchase the listing, since only they can see it.
Like Rachel said, once it's been purchased it will show up in your sold orders. And I agree with Rachel, the best designs/ideas start as custom requests from customers!
~Felie