What is the name of Japanese printing which uses hammered leaves on white cloth?
This is a hammered leaf print, or sometimes called a transfer. Flowers are also used. The Japanese name for this art is called hapa zome. It's categorized as a type of dyeing process, and hapa zome roughly translates to "leaf dye" (according to the Internet. I don't know any Japanese).

The technique is similar to the classic nature printing, which uses a roller to press the leaf into the plate receiving the transfer. For hammering, you are applying the pressure much more manually, and aren't creating an engraving that's used make additional copies.

You can find a cheap way to do this on Instructables. Here is a picture of such are done on watercolor paper: