Explanation
The first thing you need to do before you implement directory synchronization is to purchase a custom domain name. This could be the domain name that you use in your on-premise Active Directory if it's a routable domain name, for example, contoso.com.
If you use a non-routable domain name in your Active Directory, for example contoso.local, you'll need to add the routable domain name as a UPN suffix in Active Directory.
Reference:
https://docs.microsoft.com/en-us/office365/enterprise/set-up-directory-synchronization