The free Tableau Public does not allow for private data -- it will be public and accessible by anyone. However, there is a paid version, Tableau Public Premium (see Tableau Public | Tableau Software) which allows for hiding the data. Other options would include Tableau Server and Tableau Online.
(moving this discussion into the Forums)
Joshua is right on the money with his recommendation for Public Premium. Longer discussion about it here:
With Public Premium your account also gets upgraded with the ability to upload workbooks with up to 10 million rows as well as a big storage bump.