In order for departments to show up in the Department field of the Financial section of a Project, and in the lookup list for the Department attribute of the Project object, the departments must be associated to a location.
Associate the departments you have created with a location and they will show up in the lookup browse for the Department fields.
To associate a department with a location:
1. In PPM, go to Home->Departments
2. Open the affected department
3. Select the Properties drop down then 'Locations'
4. Click 'Add'
5. Click the check box next to the Location to be added, then click 'Add'