@@SERVERNAME returns name of old server

-- in the case where a server has been cloned or renamed 
-- and @@SERVERNAME still returns name of old server

use master
go

SELECT @@SERVERNAME, SERVERPROPERTY('MachineName')
GO


SELECT [server_id]
      ,[name]
      ,[product]
      ,[provider]
      ,[data_source]
  FROM [master].[sys].[servers]
GO

sp_dropserver 'OLDSERVER\OLDINSTANCE';
GO
sp_addserver 'NEWSERVER\NEWINSTANCE', local;
GO

-- has been updated in servers table
SELECT [server_id]
      ,[name]
      ,[product]
      ,[provider]
      ,[data_source]
  FROM [master].[sys].[servers]
GO

-- may need to restart instance 
-- for it to take effect for @@SERVERNAME

SELECT @@SERVERNAME, SERVERPROPERTY('MachineName')
GO