Old Domain Name showing in User Profiles

Sharepoint User Profile Sync is showing some users with our Old Domain name (from years ago).  This domain name is NOT  in our Active Directory.  I'm guessing that the profiles that show the old domain name must have been in our Sharepoint 2007 and got ported over when we upgraded to Sharepoint 2010.

This is causing conflicts and some workflows not to work (ones where its looking up a user's profile).  And when I look in Microsoft Forefront Identity Manager, there are some users listed with this error: Exception while trying to migrate user "abc\johndoe" to "xyz\johndoe"..  Microsoft.SharePoint.SPException: The user does not exist or is not unique.......

("abc" being the old domain name...and "xyz" being our current domain name)

I'm wondering what is the best way to get rid of the old domain name in our Sharepoint 2010 user profiles?  Should I update them in the User Profile database in SQL?

Does anyone know how to fix this?

Also, in Central Admin under Health monitoring, we have this message
"People search relevance is not optimized when the Active Directory has errors in the manager reporting structure. In Active Directory, only company leaders should have the 'manager' property set to NULL. As a result of errors, the Active Directory can incorrectly have the 'manager' property set to NULL for other users that can cause a decrease in people search relevance. By specifying the actual leaders of
the company, these inconsistencies are not taken into account and the relevance problem is corrected. 

Not sure if this is related.

Any help would be much appreciated... thanks!