Hi @mara2021 ,
Yes .
For both syncing on-prem AD with Office 365 and deploying hybrid,You need to register/purchase the domain name in the domain registration provider and add it to Office 365 and on-premises AD. This is different from the local AD domain you already have(mail.contoso.com) .
Additionally, to configure Exchange Hybrid, on-premises organizations need to install an SSL certificate onto their Web/Exchange server to initiate a secure session with the browser. SSL certificates need to be purchased by a trusted public certification authority (CA).
The following table outlines the minimum suggested FQDNs that should be included on certificates configured for use in a hybrid deployment.
For more information about the prerequisites for deploying a hybrid environment, you can refer to the following links:
Hybrid deployment prerequisites | Microsoft Learn
Certificate requirements for hybrid deployments | Microsoft Learn
Hope the above suggestions are helpful to you!
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