Google has fixed an issue with site names not appearing for some internal pages, this has been an issue since December 2023. I checked some examples, and they are indeed fixed - although Google said some fixes are still rolling out and those pages need to be reprocessed to be fixed.
As a reminder, Google has been battling with site name issues since it launched the site name feature in October 2022 for mobile and then site names for desktop results in March 2023. Google confirmed a known issue where the site name for internal pages may take a lot longer for Google to show properly than the home page and has now fixed that issue - months and months later.
Here was the issue:
But now it is fixed, here is a screenshot:
Google updated its site names documentation to remove this section:
Google also added, "Not seeing your preferred site name for internal pages? If your home page is already showing your preferred site name, remember to also allow time for Google to recrawl and process your internal pages."
This looks like a promising update, I am just surprised it took several months to fix.
I should note, Google still seems to have issues with some ccTLDs, like this one shows XYZ as the name name but it should be DECIPHer:
Forum discussion at X.