Rename Computer Name When Sql Server Already Installed

To rename a computer that hosts a stand-alone instance of SQL Server
•    For a renamed computer that hosts a default instance of SQL Server, run the following procedures:

sp_dropserver <old_name>
GO
sp_addserver <new_name>, local
GO
Restart the instance of SQL Server.
•    For a renamed computer that hosts a named instance of SQL Server, run the following procedures:

sp_dropserver <'old_name\instancename'>
GO
sp_addserver <'new_name\instancename'>, local
GO
Restart the instance of SQL Server.
 After the Renaming Operation
________________________________________
After a computer has been renamed, any connections that used the old computer name must connect by using the new name.
To verify that the renaming operation has completed successfully
•    Select information from either @@SERVERNAME or sys.servers. The @@SERVERNAME function will return the new name, and the sys.servers table will show the new name. The following example shows the use of @@SERVERNAME.

SELECT @@SERVERNAME AS 'Server Name'