You can make a strong suggestion on what Google should use by implementing Website Schema. This isn't a directive - Google is under no obligation to use your suggestion - but it usually works if you're patient and persistent. I've found frequently changing the exact text of these tags doesn't go down well at all.
Other methods for getting Google to pick up the name are by putting it as the Home Page title, having it follow page titles (My Article - BrandName), used in the H1 for the main page and placing it in the opengraph tags for og:site_name.
Do all of those and Google usually picks it up in a few weeks. It can fluctuate but the longer you have this information up the stronger the suggestion is.
Quoted from Provide a site name to Google Search - Google Search Central:
How site names in Google Search are created
Google's generation of site names on the Google Search results page is completely automated and takes into account both the content of a site and references to it that appear on the web. The goal of the site name is to best represent and describe the source of each result.
Google Search uses a number of sources from a site's home page to automatically determine site names, including:
While we can't manually change site names for individual sites, we're always working to make them as accurate as possible. You can help improve the quality of the site name that's displayed for your page by adding
WebSite structured data.