What is name of process used to change sample bit depth?
You are referring to "scaling". To go from 16 bits (arithmetic data, of course, not logical) to 8 is done by dividing by 256.

In some cases it's done by truncation, where the lsb's are simply discarded. If you want to be careful, you apply rounding to the lsb of the result, but then the result is the same as scaling.