I doubt there's a specific name for that particular type of formation. Call it whatever you want. "Patya's Formation" has a nice ring to it.
I can't tell what type of rock it is from the photos.
The most likely explanation is that it is igneous rock that formed in older, softer rock. It could be that some older rock got pushed deep underground and cracked due to tectonic movement--the slow, imperceptable but unceasing movement of rock caused by shifting geological plates--leaving large voids in the area. Magma came in the fill these voids created by the shifting rock and cooled, solidifying into basalt, diorite, or any number of other dense, intrusive rock types.
Eventually, whatever tectonic forces pushed the rock down into the subsurface abated, and the slow but constant process of weathering and erosion took over. Over time, everything covering these rocks wore away and this area returned to the surface. Once at the surface, all the softer rock surrounding this intrusive material weathered away more quickly, leaving these rocks behind.
The cracks are formed by stresses placed on the rock over time by the compression and extension of the tectonic plates over many millions of years.