Early on it its existence, the NSDAP (Nationalsozialistische Deutsche Arbeiterpartei, or German Worker's Party) had a 25-point program that contained many demands recognized as socialist at the time, such as the redistribution of land and the nationalization of industry. However, this was mostly included to appeal to the working class in Germany, as socialism was a powerful political force at the time. The Nazis proceeded to enact none of these policies when they came into power.

Adolf Hitler was vehemently anti-communist and anti-socialist, and he viewed everyone on the Left as enemies often grouped under what the Nazis called "Judeo-Bolshevism." One way to view this divide is that most socialists were anti-nationalist, whereas the Nazis were hyper-nationalist. Some of the first targets of the Nazis in the mid-1930s were socialist opposition leaders, many of whom were shot by SA or arrested and put in concentration camps.

Another problem for the "it's in the name" argument is Nazi economic practices in office.

While these were quite heterodox in comparison to the economic orthodoxy of the time, employing heavy state intervention to manage the process of rearmament they were fundamentally oriented around a capitalist production system. Private ownership of the means of production was preserved and in some cases extended: an early instance of privatisation emerges under the Nazis, who sold off large firms nationalised by the Weimar Republic in the early 1930s. It's from contemporary studies of Nazi economic policy that 'privatisation' enters the English lexicon via German '‘reprivatisierung’'.

As well as being the recipient of significant financial support in the early 30s, in government the Nazis relied on the support of Germany's business elite. While the interests of the two didn't perfectly dovetail - German business elites were internationalist and tended to oppose Nazi autarchic policies - there was common ground in practical areas like labour and wages policy and broad support for an authoritarian, rearmed Germany. Nazi rule was also quite profitable both in general economic terms and for well-connected firms working in key industrial sectors.

All of this is quite hard to reconcile with any useful definition of socialism.

Sources:

Tooze, Adam The Wages of Destruction: the Making and Breaking of the Nazi War Economy

Bel, Germà 'Against the mainstream: Nazi privatization in 1930s Germany' Economic History Review, 63, 1 (2010), pp. 34–55