You've renamed the server itself. Now it's time to rename SQL instances from within SQL. You'll need to reboot the services after the rename.
Let's see what the whole picture is now by running this.
EXEC sp_helpserver
Get the old servername to use to drop it.
SELECT srvname AS OldServerName FROM master.dbo.sysservers WHERE srvid=0
Check the name of the server as it is now to use to create the new SQL instance name.
EXEC master.dbo.xp_getnetname
Now we have enough information to change the name. e.g.
EXEC master.dbo.sp_dropserver 'SQLOld\I2K'
EXEC master.dbo.sp_addserver 'SQLNew\I2K','local'
Running this should show the old server name until we restart the SQL Services.
SELECT @@SERVERNAME
— results in SQLOld\I2K
Stop and restart the SQL Server services.
— results in SQLNew\I2K