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. Danny Sullivan, Google's Search Liaison, responded to my complaints about site name issues, saying the site is doing everything right and that Google will investigate what it can do on its end to fix those issues.
Keep in mind, this is in addition to internal pages being known to be slower to update when it comes to site names. But Google did say in September they saw a massive improvement with site name issue. In May 2023, Google began to support subdomains as well as domains, but not subdirectories. In July, Google pushed a bigger update to improve the Site names to show them more accurately. Google also as of earlier this month supports site names in all languages.
But Sullivan wrote in two different Google Webmaster Help Forum threads that he will pass along the issues spotted because it seems the site owners did everything right.
He wrote:
Seems like you have things in place properly; I'll pass this along to the team to see if there are some general improvements we might find to make from looking at this.
It's MHP when I look at it. I think you said previously this was something more happening in German, which, I get, is a primary concern. But the fact I'm seeing it correctly in English suggests that it should be working through our systems. I'll pass this on to see if we can find any further general improvements.
Other than what's on the docs, nothing more to do. I do see what looks like a nice implementation. Sorry about this. I'll pass the feedback on for general improvement review.
Danny Sullivan has been on these site name issues since day one and he responds to a ton of complaints in the forums. It is great to see he is still on it and working out the outliers and kinks with them.
Forum discussion at Google Webmaster Help Forum.