>> how to actually use that to instigate this change in the TextField
It's not obvious which piece of this you are asking about. You need to:
a. Set up, at an appropriately early time, an observation of the notification. The observation has an associated closure that is invoked to "deliver" the notification to you.
b. The receiver of the notification has to be (or has to know how to find) an object that has a reference to the text field. Typically, the reference would be an "outlet", and would be held by a view controller, or some controller doing a similar job.
c. The controller needs to know how to find the correct string value corresponding to the selected entity. This can be from other state maintained in the controller (and already updated as a result of the selection).
d. The controller can then update the value of the text field.
Which part of that is giving you trouble?
A couple of other comments, which you are free to ignore:
— Core Data is notoriously difficult to use, especially if you're new to Cocoa generally. Yes, it has an overall conceptual coherence, but its actual behavior tends to get more and more inscrutable the deeper you get into the weeds. If it suits you, that's great. If not, it's probably not your fault.
— You seem to be abusing NSComboBox somewhat. A NSComboBox is a kind of text field, not a kind of menu. That means, in particular, it's not really intended to constrain a user to a fixed list of things. (In your description, you add new items via a separate UI, not the combo box itself.) Things will start to get difficult if a user simply types a random string into the combo box, instead of choose a preset string. The correct control is probably a popup menu, NSPopUpButton.
If you use a popup menu, then you likely don't need to use notifications to find out what was chosen. Instead, you can give each menu item its own action (or, since it's dynamic, the same action, and distinguishing between items via their "tag" property).