Hi Jerry,
Thanks for the assistance.
As a test, I renamed the username for an account and forced a sync. Here's the screen shots for that sync. There are no reported errors in the sync.
Please note that the 2nd and 3rd steps of the sync have nothing listed under "Connection Status". Is that normal?
The last 2 screenshots show that, after the sync, the username in AD is not the same as Office 365.
Here's the account in AD
Here's the account in Office 365 after the sync