Recently Google updated the design of the search results on desktop.
The big difference is that they are now showing the favicons for each site (favicon = favorites icon).
You can see a few of them in the above search.
They let you add a bit of branding and color to the search results. Though I see a lot of Shopify stores missing favicons or using Shopify’s default favicon still.
To see what Google’s showing for you, just perform any search where your store will show up.
To add or change them, look in your theme. Specifically your theme customization and theme settings.
If your theme doesn’t support that, contact your theme developer and see if they can help you.
Though favicons don’t have anything to do with Rich Results they work similarly by making your results more attractive to searchers. They are definitely worth the few minutes of effort to setup if you don’t have it already. Even if Google later removes them or changes the design again.
And if you combine them with the Rich Results from JSON-LD for SEO you could get your search results looking really nice.
Like a sharp dress store.
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