Following is a T-SQL script you can use to rename your SQL Server after you have changed the computer name. This script will work if you are connected to the default instance or a named instance. After running the script, you must restart SQL Server for the action to complete.
DECLARE @machinename sysname,
@servername sysname,
@instancename sysname
SELECT
@instancename =
CASE WHEN charindex('\', @@servername) = 0 THEN ''
ELSE SUBSTRING(@@servername, CHARINDEX('\', @@servername), (len(@@servername)+ 1) - CHARINDEX('\', @@servername))
END
SET @machinename = convert(nvarchar(100), serverproperty('machinename')) + @instancename;
EXEC sp_dropserver @@servername;
EXEC sp_addserver @machinename, 'local'
print 'renamed to ' + @machinename
IMPORTANT:
Stop and start the SQL Server to complete the process