I want to add additional ticket statuses, or rename current statuses, for submitting tickets. Is it possible to edit the system status field to add these custom statuses?
It is not possible to edit the system status field by adding new statuses or changing the location.
However, you can create a custom ticket field to track any custom status you want to include in your workflow. For a guide on creating custom ticket fields, see the article: Adding custom fields to your tickets and support request forms.