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Hello @kurapika,
Thank you for contacting the support.
The site name in the SERPs is taken from the WebSite Schema. You can add the name of your site in WP Dashboard > Rank Math > Titles & Meta > Local SEO > WebSite Name and our plugin will add it to the Schema.
Once done, you will have to wait for Google to crawl the site again and decide to show it in the SERPs.
Hope that helps.
