Simply login to cPanel and click the Anonymous FTP icon. Uncheck both boxes (“Allow anonymous access…” and “Allow anonymous upload…”) and click the Save Settings button.
You will see email@example.com and firstname.lastname@example.org in your cPanel, but they are not enabled if both boxes under Anonymous FTP are unchecked.
If you are connecting and see a ‘pub’ folder, then anonymous FTP is not enabled. (That folder is not on your account; it is on the server.)