Google search website meta title

I believe you are referring to the %site_title% – %post-name% in the browser tab. If so, you can change the first part of that under the WP Dashboard under “Settings > General” and change site title there. This can also be done in the site editor > site identity if you want.

Additionally, if you would like to change something for this in Rank Math, I believe you’ll find that under WP Dashboard > Rank Math SEO > Titles & Meta

I think you mean site names (as Google calls them). See: https://developers.google.com/search/docs/appearance/site-names

You can influence this with the help of your SEO plugin. I would therefore recommend that you contact the Rank Math support forum: https://projectdmc.org/support/plugin/seo-by-rank-math/

Thread continues at https://projectdmc.org/support/topic/how-to-provide-a-site-name-to-google-search/