You can customize the statuses for Changes and Incidents, but you can't add custom Status options for Problems currently.
I would like the option to be added to create custom stats options for problems just like the options for changes and incidents.
For example if the problem is no longer pending anyone at your organization, but isn't necessarily closed, on hold, pending change, or a known issue I would like to add something like "Pending Vendor" so I know that the problem hasn't been fixed, but it is pending a vendor specifically.