What is this thing called that holds the gear shift cable (not the wire)? There is a small metal part that keeps the gear shift cable in place, so the inside cable can move without the cable hose moving as well. I think I damaged it slightly when making repairs so I need a new one, but I have no idea how that part is called or if it is something specific to my bike. I have a Shimano Nexus 8 internal shifter.

I attached a photo of the part standalone and installed.
In Shimano-ese, it is part of the "Outer Receiving Unit." 



You can pull up the exploded view diagram for you specific hub model on techdocs.shimano.com to corroborate what you need. Then you can google around for "shimano outer receiving unit" and get the right part number for your hub on the off chance that it's different for the different Shimano internal hubs.