Read Google's guidelines on how to make your favicons eligible for inclusion in search results.
A favicon isn't guaranteed in Google Search results, even if all guidelines are met.
Google Search only supports one favicon per site, where a site is defined by the hostname.
Your favicon must be a multiple of 48px square, for example: 48x48px, 96x96px, 144x144px and so on. SVG files don't have a specific size. Any valid favicon format is supported.
Icons are automatically scaled to 16x16 where needed. CAUTION: Do NOT provide a 16x16 icon yourself. Let Google generate its own, from your 48x48 version.
Google looks for and updates your favicon whenever it crawls your home page. If you make changes to your favicon and want to inform Google about the changes, you can request indexing of your site's homepage. Updates can take a few days or longer to appear in search results.