The German word for “national” is definitely not spelled with the letter Z , it’s spelled the same as in English, the reason it’s called Nazi party is because in Germany socialists ( Sozialisten) are commonly referred to as “Sozis”, so the combination is “Nationalist” and “Sozi” or “Sozialist”= Nazi.
And Adolf Hitler didn’t propose that name anyway, The party was initially called German Worker’s Party ( DAP =deutsche Arbeiterparty) and the executive committee , following Rudolf Jung’s recommendation, changed the name to NSDAP, adding the words National and Socialist , both over Hitler’s objections. Hitler wanted the name to be “Social Revolutionary Party”. However, RudolfJung, having written a book on “National Socialism” a book he hoped was going to be as important to Nazi ideology as “Das Kapital” was to Marxism/ Socialism, was able to convince Hitler to go along with the new party name. The word “Socialism” was indeed added to attract left-wing workers, but it was, of course a 'bait’n’switch" since Nazis were definitely anti socialist, ant-communist and anti-marxist.