The new inbox doesn't show the parent task name on the main view (important/other) when a notification is for a subtask. (Old notifications did.) You can get to it by clicking into the notification, but it would be preferred to have that at-a-glance insight.
We often put the client name on the parent task and don't put it on the subtasks to avoid redundancy. (Also because of template limitations.) So a person can be assigned several tasks named the same thing. It would be really nice to be able to see parent task name in the main view.