Name for turning ingredients to powder / mush, and then molding back into their original shape
Reformed

This is most often used to describe meat products such as "reformed ham" or "reformed scampi". You can occasionally see onion rings made with chopped onion described as reformed, e.g. here. 

Pringles could be described as "reformed potato snacks" for example. Pringles are less than half potato though, so that may not be entirely accurate.

As for doing this at home, it's common to bake a potato, scoop the potato from the skin, mash it up with some seasonings and then put it back in the skin, thereby reforming the potato.