The site you build with Hello Website Builder can always be accessed from the free Hello Website Builder’s domain and will never expire. You can configure the free Hello Website Builder’s domain from SETTINGS > Domains in Site Editor. Read Using Hello Website Builder’s Domains to learn how.
You can also hide the Hello Website Builder’s domain from your visitors by connecting a domain you own from a third-party domain provider to your Hello Website Builder’s site and setting this connected third-party domain as primary.
If your built-in domain is still displayed after making a connected third-party domain primary, you can ask Google to update your site by submitting it to Google Search Console for re-indexing. The same principle applies to other search engines which you can also contact with the request to re-index your site.