"Our four months' activities at meetings up to January, 1920, had slowly enabled us to save up the small means that we needed for printing our first leaflet, our first poster, and our [Nazi] program."
This suggests to me the German Worker's Party was renamed the National Socialist German Worker's Party sometime around October 1919, or even earlier.
I know that it's common to hear it originated February 24th, 1920, because that's when they declared their goals to the public but their first actual public meeting was February 4th, 7:30 A.M.
Thanks for the help.