Hello @markk26,
Thank you for contacting Rank Math support.
Google uses different sources to figure out and show your Site Name on SERPs
- og:site_name
- Website structured data (Schema)
- Content in title elements
- Heading elements, like H1
Among them, Rank Math automatically includes og:site_name, meta tag and the Website Schema on your page. You can also check the Google documentation on site-name: https://developers.google.com/search/docs/appearance/site-names
However, as mentioned in the documentation, this process is automated by the algorithm, and even though it takes into account the information on the website, it is still not guaranteed that your site name will come up correctly in Google SERPs since it’s solely decided by Google what they found relevant and user-friendly and which one they want to show.
You should wait for Google to decide to show the name in the SERPs.
Please do not hesitate to let us know if you need our assistance with anything else.