Answer
To sanitize the primary user information on a computer, so that is starts fresh - the following steps must be performed:

Client Side

1.    Stop the Altiris Agent
2.    Delete the following registry key: HKEY_LOCAL_MACHINE\Software\Altiris\Altiris Agent\Inventory\PrimaryUser
3.    Delete the following file: %ProgramFiles%\Altiris\Altiris Agent\AeXUserMonitorLog.xml
4.    Start the Altiris Agent
5.    Force Basic Inventory to run on the client

Check the Resource Manager for this machine and if it is still incorrect you may need to delete the computer from the console to allow it to send in fresh inventory again.