@PM I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this! Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to "Accept " the answer.
Issue: Azure AD Sync - Distribution Group - Incorrect Properties, After synchronization, I do see an object that appears in Microsoft 365. But, the name and email are just long strings of seemingly random characters. I know this is the sync'd distribution group because of the group membership.
Solution: Resolved by PM and below are the steps
there was a public folder that was synchronizing, and it had that e-mail address. The public folder was not visible in teh Azure or M365 console GUIs.
As I mentioned, the synchronized object had a strange name. I got the Object ID and ran this command:
$errors = (Get-MsolGroup –ObjectID [ENTER ID HERE]).Errors
$errors | foreach-object {"`nService: "+ $.ErrorDetail.Name.split("/")[0]; "Error Message: "+ $.ErrorDetail.ObjectErrors.ErrorRecord.ErrorDescription}
The output helped me to learn that an existing object with that e-mail address and\or UPN already existed. Then I ran:
Get-Recipient | where {$_.EmailAddresses -match "******@company.com"} | fL Name, Recipienttype,emailaddresses
The output showed me a public folder.
Then, I ran disable-MailPublicFolder -Identity "TaxDeptFax".
Then, I re-created the distro group in the on-prem AD, and it sync'd properly.