A Workforce for ArcGIS project is based on a predefined schema. This schema states that assignment types are populated into an associated coded value domain on the Assignments feature layer when created.
Sometimes assignment types need to be modified, perhaps because of a typo. On the Workforce front end, it is impossible to edit an assignment type. It can only be deleted (if the type is not being used by an assignment).
One can work around this by opening the Workforce project in ArcGIS Online, open the Assignment layer properties and directly edit the coded value domain.