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Google added new documentation which describes how you can use WebSite structured data to indicate your preferred site name, which currently appear in mobile Google Search results for the following languages: English, French, Japanese, and German.
They clarified that the generation of site names on the Google Search results page is completely automated and takes into account both the content of a site and references to it that appear on the web.
They use a number of sources from a site's homepage to automatically determine site names, including:
You can help improve the quality of the site name that's displayed for your page by adding WebSite structured data.