You can have it done by a psychologist or psychiatrist. This is what I have learned from others. I have not had the test done officially though, I did the online tests and the results did not surprise me, so I don't see the need to have an official certificate of aspergers since it is not considered a disability.
No, they won't tell anyone, there is patient client confidentiality. They can only disclose this if there is a court warrant if you committed a crime and they want your mental history.