Favicon
From this platform's help center:
Add a custom favicon
In a browser, like Chrome or Safari, the favicon is an image that shows next to a site's name at the top. Your site needs to be live to show a favicon.
On your computer, open a site in new Google Sites.
In the top right corner, click Settings Settings.
In the "Settings" window, go to Brand Images.
Under the “Favicon” section, click Upload or Select.
Choose a .jpg, .png, or .gif file.
Choose a file and click Open or Select.
At the top right, click Publish.
I'm including this because of an email Yandex sent me.
Didn't have time to really get into it... seeing as I was working under my 10 day odessey thingie, and I didn't even know what a favicon was.
UPDATE
A favicon shows up on browser tags and bookmarks.
To upload or edit, hit the gear icon (settings) on the upper right-hand corner of the screen.
Select "Brand images".
Scroll down to the Favicon section and upload an image.