How to change SQL Server security groups name after server rename?

Question

A Windows 2003 server has been renamed from LAMDAMIRROR1A to LAMDAMIRROR2A and the following
sql has been run in SQL Server 2008 R2 on the server :
exec sp_dropserver 'LAMDAMIRROR1A'
exec sp_addserver 'LAMDAMIRROR2A','local'
However, although everything appears ok, the 5 Windows 2003 Groups (automatically created by
the SQL 2008 R2 Install) still contain 'LAMDAMIRROR1A' in their name. Does this matter ? Can the Windows Groups be just renamed (right click , rename) or will this cause problems ?
The Windows Groups are :
SQLServer2005SQLBrowserUser$LAMDAMIRROR1A
SQLServerDTSUser$LAMDAMIRROR1A
SQLServerMSSQLServerADHelperUser$LAMDAMIRROR1A
SQLServerMSSQLUser$LAMDAMIRROR1A
SQLServerSQLAgentUser$LAMDAMIRROR1A
There are also Registry entries containing the old 'LAMDAMIRROR1A' name. Does this matter ?
Should this be changed ?
eg. 
My Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Microsoft SQL Server\100\Machines\OriginalMachineName.
My Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Microsoft SQL Server\Services\Report Server\GroupPrefix.
My Computer\HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Print\printers\Microsoft XPS
DocumentWriter\DsSpooler\serverName.
etc

Answer 1

Hi,
If you have executed the sp_dropserver and sp_addserver in SQL Server 2008 R2, we need to verify if you renamed the SQL Server instance successfully. You can select information from @@SERVERNAME or sys.servers to verify if the renaming operation is completely
successful in SQL Server Management Studio (SSMS). If yes, whether you change the registry entries containing the old 'LAMDAMIRROR1A' name or not, there’s no impact on SQL Server Services. For more details, please review this article: 
How to: Rename a Computer that Hosts a Stand-Alone Instance of SQL Server.
In addition, if you must rename the windows groups, you can just right-click the group in Computer Management/System Tools/Local Users and Groups/Groups and rename it, or you can create new groups with new names, for more details, please review this article:
Manage Local Groups. If there are some issues regards the Windows, you can post the question in the Windows Server forums at
http://social.technet.microsoft.com/Forums/windowsserver/en-US/home?category=windowsserver . It is appropriate and more experts will assist you.
Thanks                 
Lydia Zhang