Any tips for when the user definitely know it's your product? I can't think of anything besides starting with butchering some aspect of it. Then again that might trigger some empathetic response, and end with even less actionable feedback.
I think people can't un-know something, so I'd try very hard to get test subjects in a way where they don't think the people they are talking to are the ones who make the product.
For example, you could set up a fake market research org, and have them say they are "conducting a study on [your market] and are looking for users of products like [competitor 1], [competitor 2], and [your product]". Then for the user testing sessions you could rent a conference room from somebody like Regus, or even rent a user testing lab. Then during the tests, make sure to start with general questions and test (or show screens from) the other products before you get to testing yours.
I'm not sure if those specifics will work in your environment, but I hope you see what I mean.
