Google is officially rolling out the new site name and favicon design, along with the new sponsored ad label, in the mobile search results. Yes, this is something Google has been testing and we saw this coming but now it is official and live in English, French, Japanese, and German regions.
The site name will show up at the top of the search result snippet, on the right of the new larger favicon, and above the URL of the search result snippet. Here is a GIF of this new design in action:
Google also made this illustration:
Google wrote they have added the "site names to search results on mobile, so you can easily identify the website that's associated with each result at a glance." Google also updated the size and shape of the favicon that appears in Google Search, also with the goal to make it easier to see on the page.
Google has new site name structured data documentation that you can specify so that you can help control what Google shows for your site name. Google said that it "relies on a variety of sources to identify the site name for a search result." But if you want to indicate your preferred site name, you can use structured data on your homepage to tell Google what the site name should be, Google explained.
Google said the Site names are currently available for mobile search results in English, French, Japanese, and German, and will be rolling out to additional languages over the next few months.
Google also said it recommends revisiting the documentation for favicons for the latest best practices. Google said it will continue to recommend providing an icon that is at least 48px, and follows the existing Google favicon guidelines.
Google is also taking feedback on this in the Google Web Search Help Forums.
Forum discussion at Twitter & Google Web Search Help Forums.
Note: This was pre-written and scheduled to be posted today, I am currently offline for Simchat Torah.