Question: Do the filenames associated with a DICOM image series (from a single scan) match the spatial ordering? What I mean is if the patient was scanned “head first” is 000000.dcm more “superior” than 000001.dcm which is more superior than 000003.dcm etc? If the answer is no, how is spatial ordering established?

Answer: 
No, the file names are rarely associated with the spatial ordering.

The best thing to use is the image position (patient) (0020,0032) and image orientation (patient) (0020,0037) values to get the geometry of each image. From there, you can "order" things how you wish, spatially.
You might want to have a look at these links:

[How to compare coordinates of different series 1](https://stackoverflow.com/questions/36996353/finding-the-coordinates-mm-of-identical-slice-locations-for-two-mr-datasets-ac/36997168#36997168)

[How to compare coordinates of different series 2](https://stackoverflow.com/questions/37322856/interpolation-between-two-images-with-different-pixelsize/37339630#37339630)

[DICOM attributes used for calculating affine transformation](http://dicom.nema.org/medical/dicom/current/output/chtml/part03/sect_C.7.6.2.html)

[Recommended reading on DICOM in general and segregation of orientations](https://stackoverflow.com/questions/34782409/understanding-dicom-image-attributes-to-get-axial-coronal-sagittal-cuts/34783893#34783893)