Sanchi Dua This is a "Retrospective Cross-Sectional Study". You may find it useful in here. ( http://medicine.emory.edu/documents/research/kalogeropoulos-study-design-talk.pdf )
Yes, but it relies on (good) public registers, the word 'retrospective' should be down-toned. Is also a cohort, not just cross-sectional. Finally, it is not a sample but a geographically defined 'complete population study.' So 'complete-population cohort' is a a suitable designation.
The question here is not what you call it, but what it is - by virtue of what was done.