If you are running in a non-messaging (Exchange 2000 or higher) Active Directory environment, and you want to use the Microsoft Online Services Directory Synchronization Tool, you must configure certain Active Directory User attributes if you want the User Login User Principal Names (UPNs) to be consistent with what is being used in the on-premise Active Directory environment.

For Example: an on-premise Active Directory using the Domain Namespace of Contoso.com that has users with a login UPN of user@contoso.com.  There is no Exchange 2000 messaging environment within this Active Directory, however user objects have their MAIL attribute configured, so they are mail enabled.  This MAIL attribute is used in a Non-Exchange AD environment when running DirSync wheto create new Microsoft Online Users.

To mirror the on-premise User Login with what is used in the Microsoft Online Company environment

1. Create a Microsoft Online Service Domain name.  Use the same name as the on-premise environment, e.g Contoso.com
2. Verify this Microsoft Online Service Domain name, which proves ownership and allows a Microsoft Online Services administrator to create new users for this Domain, and to provide or add SMTP addresses for existing users.
3. Set this Domain name as Default.  As new users are created and/or Directory Synchronized, their accounts and email address will use this Domain (Online user's will always have a secondary Email Proxy address of companyX.microsoftonline.com, which is provided as a Default Routing Domain, created during the Online Company's Provisioning process).
4. Modify/Add on-premise Active Directory User object's MAIL attribute with an e-mail address that was previously created and verified (e.g. user@Contoso.com)
5. Run the Microsoft Online Services Directory Synchronization Tool, which will replicate all Mail and Mailbox enabled users/groups into the Microsoft Online Company as Deactivated Users.

Note:  From this point, a Microsoft Online Services Company admininistrator can Activate these users.  They will granted services by the Online administrator. Their Login UPN and default SMTP address will be user@contoso.com instead of the default user@Contoso1.microsoftonline.com.