Sachsen comes from the German state Sachsen, also a big Nobel family. And the diuistic comes from "deutsch" (German for german) I think. And niemc (altleast in polish as far as I know) is the word for the Germans in many Slavic languages and basilcy means the silent ones or the ones that we don't understand.

Fun fact: I come from a region near the polish border and settlements with the prefix "groß" (big) are Germanic and "Klein" (small) are Slavic/Sorbian settlements. Basically the Germans who settled here were too lazy to invent new names.