Actually I am not sure if there is a specific name for such a case. If anything it would simply be listed or labeled as a SFF case. Direct meaning being that the case would be too small fit in larger motherboards.
For the most part, any given case should list the size(s) of motherboards the case will support.
You can install a smaller motherboard in a bigger case if the case provides the necessary standoff locations.
That said: You know the form factor for the motherboard. Find a case (or cases) that meet your requirements and check the case specs to determine if the case does indeed provide/support Small Form Factor motherboards.
My general thought is that there is little harm in using a larger case. Easier to work in, route cables, better airflows (cooling).
Just my thoughts and hopefully there will be other ideas and suggestions offered.