If I understand correctly, your domain name is being used as the site name. According to?Google’s documentation, it uses several different sources to determine the site name automatically, and you can indicate your preference by adding?WebSite?structured data. The?WebSite?node is a parent piece of the?Web Page?schema. You can see more information about this at?https://developer.yoast.com/features/schema/pieces/website/.

I ran your site URL through Google’s?rich result test tool,?and I can confirm that Yoast SEO is outputting the necessary schema to show your site name in search results instead of the site URL.?See screenshot.

Since you have everything set up correctly, please allow time for re-crawling and re-indexing. Remember that it may take a while for Google to find and crawl it. For general questions about crawling and indexing, check the Google Search crawling and indexing FAQ.

If the issue persists, please post a question in the Google Search Central Help Community.