The word Nazi was invented by Konrad Heiden in the 20s and was used with a negative connotation. Heiden, a Journalist and Democratic Socialist with Jewish ancestry, created it as a spinoff of the name used for the marxist SDP which was "Sozi". Its also a pun similar to the word for "simpleton" in Austro-Bavarian. It came into usage in other countries after a propaganda push by Jews including Heiden when he was forced to leave after the NSDAP came to power.
To my knowledge is has nothing to do with Ashkenazis.