The statuses of a caregiver are hard coded, meaning they cannot be changed. The reason for this is a LOT of the logic of the system/reports are based on the caregiver's status. That being said, there are several drop downs in Bluesky which can be changed in Admin-System Lists. Caregiver status is just not one.
You can post this as an idea, if other users vote it up, it gets implemented. You can do this by clicking on the Question Mark in your system. Then click "help us to decide what to add next." Say that you want this, and then others vote on it.
I hope this helps out.