Data Collector Component Name Doesn't Change After Updating SQL Server Name
I cloned an MS SQL server, and changed the name of the machine and SQL
  server, but the old name continues to show up as a component name in
  the disk usage data collector, which I believe is what's causing that
  job to fail
  
  However, SELECT @@SERVERNAME brings up a NULL value, despite
  restarting the server.
  
  How do I change the component name?


Give this a shot since you state SELECT @@SERVERNAME brings up a NULL value, despite restarting the server.

1. Run the below with the local as the second argument. . .

TSQL

SP_DROPSERVER
GO
SP_ADDSERVER 'NewServerName', local
GO


2. Restart SQL Server (if you can restart the server OS meaning power cycle it)

3. Run the below once it's back up and confirm . . .

TSQL

SELECT @@SERVERNAME 
SELECT SERVERPROPERTY('ServerName') 


4. If the values are correct, then rerun your SSIS process and see if that resolves it as well.



SP_ADDSERVER


  [ @local = ] 'LOCAL' Specifies that the server that is being added as a local server. @local is varchar(10), with a default of NULL.
  Specifying @local as LOCAL defines @server as the name of the local
  server and causes the @@SERVERNAME function to return the value of
  server.
  
  SQL Server Setup sets this variable to the computer name during
  installation. By default, the computer name is the way users connect
  to an instance of SQL Server without requiring additional
  configuration.
  
  The local definition takes effect only after the Database Engine is
  restarted. Only one local server can be defined in each instance of
  the Database Engine.