You probably do not have a signatory attached to the organization record.  To add a signatory, create an organization contact in the organization record with the Signatory attribute enabled.  Open the organization record, then go to the Contacts tab. Under All Organization Contacts, click Add Contact at the bottom right, and create your organization contact profile. Check the Signatory attribute and any others that apply then click Save and Continue. At this point you can go back to the process record (Process Details tab -> Other Info section) and you should be able to select the organization contact in the Signatory field.