Syncing On-Premises AD User Accounts with Azure AD Connect

Question

There is a need to align on-premises Active Directory (AD) user accounts with Azure AD through Azure AD Connect. The current setup involves syncing a specific Organizational Unit (OU), but the issue arises due to differing domain names. The on-premises domain is example.gov, while the Office 365 domain is example.com, which is a registered public domain.

User accounts on the domain controller are formatted as lastName_Initial (e.g., ******@example.gov), whereas the corresponding email addresses are structured as FirstName_LastName@example.com.

When syncing with Azure AD Connect, the user information populated shows the on-premises domain (example.gov). In previous versions of Azure AD Sync, adjusting the userProxyAddress to include SMTP:user@example.com allowed the sync to recognize this as the user's email. However, the current configuration results in Azure Connect creating new users with usernames in the format ******@example.onmicrosoft.com when the proxy address is not added.

Adding the proxy address does not seem to resolve this issue as it did previously. The goal is to ensure that the AD user accounts mirror the Office 365 accounts without the need for manual changes in Entra ID for each user. What steps can be taken in the sync process to achieve this?