Rename SQL Server

We are working with customer. As part of requirement we faced this problem.
Step1: Actual hostname is COMPUTER1 then renamed to SYSTEM123.
Step2: Rebooted Server.
Step3: Through SSMS i executed below command
sp_dropserver 'COMPUTER1'
GO
sp_addserver 'SYSTEM123', local
GO
Step4: Restarted SQL Services
Step5: Then i executed @@servername, it's still showing old name (COMPUTER1)
Step6: Again i executed above script, then i got error message that COMPUTER1 doesn't exist, use sp_helpserver 
Step6: when i execute sp_helpserver, it showing hostname as SYSTME123.
Step7: Then we handovered server to Customer,
Finally customer confirmed that it was not renamed still showing old name (COMPUTER1).
Please help me where went wrong? is anything wrong in above procedure.