Nationalizing institutions does not meant the countries economic system is socialism. The US has nationalized private posts, railroads, telephone companies, and electric power companies and has instituted price controls. That does make the US a socialist country.
The German Workers Party was renamed to the National Socialist German Workers' Party in order to gain support of the trade unions which Hitler hated and later destroyed.
Nazism is traditionally held to be an extreme right-wing ideology, the party’s conspicuous use of the term “socialist”, which refers to a political system normally plotted on the far-left end of the ideological spectrum has long been a source of confusion. The assumption that because the word “socialist” appeared in the party’s name and socialist words and ideas popped up in the writings and speeches of top Nazis then they must have been actual socialists is naive and does not match the facts.
This is very good post.
Socialism inevitably leads to taking control of means of production by nationalization, because that is purpose of socialism. Although it's true that US throughout the history used nationalization of properties and businesses, it did it with different reasons.
During WWI, all US railroads were operated (not owned) by Railroad Administration as a wartime measure and were return to private control after war. The same happened with telephone systems that were under control of US government for about a year. Amtrak was created for the purpose of relieving privately own railroads of legal obligation to provide passenger service that was not profitable.
You said that German Worker Party changed name to gain support of trade unions. If that is only reason, and if they were not socialists, there wouldn't be a reason to keep "socialist" in their name after they had full control of the government beyond 1933.
Despite having declared, at various times, “I am a socialist,” “We are socialists,” and similar avowals, on a personal level, Hitler displayed little regard for the actual tenets of socialism, or, for that matter, socialists themselves. In order to prepare the country for the struggle he saw to coming, he nationalized much of the country's institutions but also leaving much of industry in private hands. He left in place capitalism when it served his needs. Hitler upheld ownership of private property, individual entrepreneurship, and economic competition, and disapproved of trade unions and workers’ interference in the freedom of owners and managers to run their concerns. Capitalism was, therefore, left in place. Hitler was certainly no socialist; a fascist, a right wing nationalist, and a dictator, yes.
You claim that Hitler kept ownership of private properties and companies in private hands. It sure appeared that way, but the German government, not the owners, exercised powers of ownership by deciding what is to be produced, in what quantities, how, and what were the prices of the products, and wages of the workers producing it. Most of the owners of those properties and companies were part of the German government, not by choice, but by necessity of their own survival.
You're overlooking another aspect of socialism, where common good comes before private good, and that individual exists as the means required by the state, in other words, individual is own by the state, and therefore individual's property as well. Just as it happened in Germany, it happened in every socialist country, since October revolution is Russia, until Venezuela, with the exactly the same outcome.