All we did was change the name the user uses to log in because a security initiative having the same log in username as their email address is inherently insecure, domain remains the same.
AD is local and we have a exchange server local but our mailboxes are hosted in O365. It is referred to as a hybrid format. In short we cannot make changes to AD or Exchange from our cloud environment only our local as changes are only made upstream and not down.
In the Microsoft 365 Admin center select the user, on the "Account" tab it shows "aliases" when you click "Manage username and email" I get the primary email address last.first@tenant .com, the username lfirst1234@tenant .com and under aliases lfirst1234@tenant .com and lfirst1234@tenant .onmicrosoft.com
In the exchange admin center, select the user "General" tab and email addresses. Manage email address types and get the same values as the base 365 Admin Center.
If I go to my local Exchange server and edit the user. On the tab that is labeled "email address" I can see the value(s) SMTP last.first@tenant .com and smtp last.first@tenant .onmicrosoft.com
The last.first@tenant .onmicrosoft.com is what I need to push up to the cloud as that value is not represented in "the cloud" environment.