We have assigned one of our users (Manar) the role of CAR and NCR. He can view those screens from his account but his name does not appear in the routing workflow, so no one is able to route to him for creation, review, validation, etc.
Those drop down lists are populated based on the Workflow assignments. You should be able to go to Admin>Maintenance>Workflow Maintenance and edit the NCR/CAR assignments. You can add them to whichever State you need them to be available for routing (Creation/Validation/Review/Closed/Etc).
@robinl nailed it, anytime you’re not seeing the users you’d expect to see in the workflow assignment options, that maintenance table is the first place to check.