Starting with Sytist version 1.2 is the option to have custom favicons / icons for each gallery. This is shown in the browser tab, when bookmarked and when added to the home screen of a tablet or phone. This can be enabled in Settings -> Photo Settings.
If you are updating to version 1.2, it won't automatically create these for existing galleries. You would have to view the photos in the gallery in the admin to have them create (just viewing the photos page will create it).