The website made via your Business Profile is hosted by Google at no charge. Your website will carry a name you choose with a "business.site" web address -- for example, "yourcompanyname.business.site."
If you would like a custom domain -- for example, "yourcompanyname.com" -- you can search for a custom domain name and purchase it from Google Domains.
To purchase a custom domain for the website made via your Business Profile on Google, publish your site and click "Buy Domain" when prompted (or from the Settings menu in your account). You can then search for domain names and purchase a domain name. We will automatically connect your website to your domain name. Learn more about Google’s domain service.