Purchasing a custom domain
The site you created on Google My Business is hosted by Google for free. 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 your Google My Business website, 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.