I am after Tableau Server not Tableau Online.
Please see below respond from Tableau Support in regards to Site Specific Logos.
Unfortunately, the ability to add a variety of custom logos for individual sites on Tableau Server is currently not built into the product. Tableau Server can use custom logos for the entire server only.
I have added your request to our existing enhancement request for the Product Management team to review for possible inclusion in a future release. Though I cannot give a firm date due to the many moving parts that go into a software release. Tableau tries to maintain a frequent maintenance release cycle. Please visit our release news page for news of recent releases: http://www.tableausoftware.com/support/releases
Another option to provide suggestions for product enhancements is to submit an idea through our community: http://community.tableau.com/community/ideas Providing feedback through the community forums allows other users to vote and discuss enhancement requests, and allows our development team to gauge the demand for each enhancement.