Make sure to check out the new site name structured data documentation.
What it looks like. Here is a GIF of this new site name and favicon placement:
Availability. Site names are currently available for the Google mobile search results in English, French, Japanese, and German. Google said it will be rolling out to additional languages over the next few months. As an FYI, we saw Google testing this several weeks ago.
Controlling site names. Google explained that Google Search uses a number of ways to identify the site name for the search result. But if you want, you can use structured data on your home page to communicate to Google what the site name should be for your site. Google has specific documentation on this new Site name structured data available over here.
Upgrading the favicon. Google is also recommending revisiting the documentation for favicons for the latest best practices. Google is now also recommending you provide an icon that’s at least 48px, and follows the existing favicon guidelines.
Ads. This is also coming to ads, so the size of the site name, favicons, and also the ad label will be more prominent in mobile search. In fact, Google is rolling out the “Sponsored” label in mobile search, officially replacing the “Ads” label from Janaury 2020.
Why the change. Google said the change is to help provide “even more information about the sites that you see so you can feel confident about the websites you visit.”
Why we care. With any change to Google Search and the design of the search results, searchers may click differently. So monitor your click through rate in Google Search Console and see if you need to make changes to your site name and/or favicon to make any improvements to your click through rate from Google Search.