This is not currently a feature of Tableau Public. Tableau Public is a free service, your only options are to make a workbook private to you or public. If you need to share with clients then I suggest Tableau Online, running your own Tableau Server, or finding one of the companies that will host a Tableau Server site for you.
I have my own server, tableau should pop up to enter password before opening. Is this possible?
It is not possible.
Are you using Tableau Server? Online? Or just Desktop?