This is the name of the organization that you created when you set up your account. You can find this immediately after the domain name in the URL: e.g., for https://app.shortcut.com/honeybadger the organization name is honeybadger.
Your API Token can be found in the Shortcut UI by clicking on the gear icon for settings, choosing the Your Account link, then choosing the API Tokens link. Choose a name for your token (like Honeybadger) and click Generate Token. Copy the highlighted token, and paste that in the API Token field.
Click the Fetch project info button to make a request to the Shortcut API to get your list of projects and workflow states. This will populate and enable the remaining checkboxes on the form.
Each Honeybadger project is associated with one Shortcut project, and you can make that choice here. You can also choose which of your Shortcut workflow states will be chosen for stories when they are marked as resolved or unresolved. The stories will be updated to those states if you also enable the respective Error Events options.
Users can create stories in Shortcut by clicking the Create Story button on the error detail page in the Honeybadger UI. By default, these stories will be created as the Shortcut user whose API Token is configured in the integration settings. Users can have stories associated with their own Shortcut account by getting an API Token as described previously and adding it to their authentication settings.