Adding it is easy. Just add an .ico image file that is either 16x16 pixels or 32x32 pixels. Then, in the web pages, add <link rel="shortcut icon" href="favicon.ico" type="image/x-icon"> to the <head> element.
You can easily generate favicons here https://www.favicon.cc/
This is an accepted solution.
Nick here from Shopify!
Dawn has not yet been released to merchants and all features are not available yet at this time. I see you're a Shopify Partner (I have added this role status to your community profile) an guess you're working on a copy of Dawn in a merchants store, which we are not able to support until the theme is officially released. We don't have a date for the release just yet either! Be sure to keep an eye out for it. We will be announcing it to let all the merchants know.
Let me know if you have any other questions in the meantime.
Are you using the same theme as before? In this isntance it wouldn't automatically update in the theme like that, you would need to download it again from the theme store and it will have the favicon option!
I downloaded the theme just now and it shows up.
With regards to the theme settings on how it looks etc, you would have to set that up again, but you wouldn't need to import your products or any other settings like that in.
It would be like getting a brand new theme from scratch in this sense. It's not ideal, I know, but it would be the only way for this!
I completley understand how annoying this is @nightingalekls. Because the theme you have currently can't have that Favicon part added automatically, adding a new updated theme would be the only way to get the latest Dawn theme and editing settings.