Welcome
If you have a free subdomain and are talking about the topmost text that says “InfinityFree” / “Epizy” / etc, that is controlled by google, is based off the base domain name, and cannot be changed.
You would have to buy your own custom domain (.com can be as cheap as $11 for a year) and add it to your hosting account and to Google.
Note from @Admin:
Given how this answer is often linked to as being the “right” answer, I will clarify that it is not.
cannot be changed
This is not true. The site name is set with a separate HTML meta tag. It’s not based on the
titletag, which contains the page title, not the site title. If you don’t specify your own site name, the site name from the base domain is used, which is InfinityFree.If you want to show your own website name, all you need to do is specify it, by adding a meta tag with the
og:site_namekey.You can read more about this in Google’s documentation.
Site Names in Google Search | Google Search Central | Documentation | Google for Developers