Hey there @Organic1617.. So there are two separate issues. Let's take them one at a time.
First, the screen shot you provided (thank you!) is from a Google search. You can change your site icon from your web dashboard > Online > Online Store > Site Preferences > Site Icon Section. It's also a good idea to check your location branding settings at your web dashboard > Settings > Locations > (select location) > Edit location. Scroll down to the Branding section and edit that as needed.
Secondly, go to your web dashboard > Online > Online Store > Website > Site Preferences. There are lots of things you should set up there to define your online/search engine preferences for your site.
Lastly, there are other SEO settings that help search engines find you easier as well as identify you better. Those can be found at your web dashboard > Online > Online store > Website > SEO. There you will find a lot of things you should set up that will be provided by Square to the various search engines. Since you mentioned the search results showing your name, I'll direct you to the "Search results preview box." Edit this to provide what the search engine shows instead of that link shown in blue in your screen shot.
I hope that helps get you started. Let me know if you need anything else.
Chip A.
Square Expert & Innovator and member of the Square Champions group. (But NOT a Square employee, just a seller like you)
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