Absolutely. On your dashboard, simply drag in an image object with your logo and place it where you want it.
Are you talking about using a 'splash page' with department logo's to navigate to the correct dashboard?
If so the basic approach is to build a sheet for each option and add an image into the view as a custom shape. Then add all those sheets onto one dashboard. A combination of this:
https://interworks.co.uk/blog/menu-navigation-within-a-tableau-workbook/ as a simple example of the dashboard should get you started.