How to leave a facebook network

*** EDITED: Unfortunately this solution does not seem to work at this stage as facebook seems to have changed their code to prevent people from being removed from their primary network. I encourage you to report this to them by filling out this form and they might eventually do it for you: http://www.facebook.com/help/contact.php?show_form=profile_bug. As a workaround, you may choose a different network, that you are ok to keep, then you can remove your old network. If anyone reading this has a solution, please feel free to comment below. I'm however keeping the original post for the sake of history tracking. ***

I might be an exception, but it did disturb me a lot to have the name of a network added under my name in facebook when looking in friend lists, such as my friend's friend list, or when you open the link of the list of people who liked a post... etc. You might just want to get rid of your primary network for other reasons (one of the simplest, not part of it anymore), but to be honest, when I tried to remove this annoying network name from below my name, I did not find a solution up until today.