What is this thing called that holds the gear shift cable (not the wire)?
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.