Hello @sanil7,
Thank you for contacting us, and sorry for any inconvenience that might have been caused due to that.
Can you please share the affected URLs where the featured image has not been indexed?
Please be advised that Google may take a while to show your URLs and the images on SERPs after you publish them to index on Google. As Google assigns a crawl budget to your website depending on various factors that directly affect how soon your content can be indexed. You can always give Google some time, and the URLs/images should get indexed by Google automatically.
For the issue with site name on SERPs, there are various sources that Google uses to define your site name on SERPs. For example, the content in og:site_name meta tag, in the schema, etc.
Hence, we’d suggest you follow the Google guidelines I’ve shared below to let Google pick the correct site name for your site.
https://developers.google.com/search/docs/appearance/site-names#how-site-names-in-google-search-are-created
To set the homepage title, go to the WordPress dashboard > Rank Math > Title & Meta > Homepage > Homepage Title, and here you can set your site name as you wish.
Next, go to WordPress dashboard > Rank Math > Title & Meta > Local SEO and set the website name and organization name for your organization, and click “Save Changes” to set the organization/local business schema.
The other option is to go to your WordPress Dashboard > Settings > General > Site Title and Tagline.
Please note that it’s still not guaranteed that your site name will come up correctly in Google SERPs, since it’s solely decided by Google what they find relevant and user-friendly and which one they want to show. The best you can do is to follow the guidelines of Google strictly.
Hope that helps, and please do not hesitate to let us know if you need our assistance with anything else.
