The official name was the National Socialist Democratic Workers Party. However this is of no use. They certainly weren't democratic, so why should we believe they were socialist? The party worked in the interests of workers by imposing price controls. The controls were on retail prices, so shopkeepers had to absorb the losses. Naziism was no friend to small business. As to state ownership of business, the party did start an arms factory named after Hermann Goering. But generally they worked with existing private enterprise. So would that mean that they were not socialist? Hitler was a pragmatist and had a record of using people for his purposes until they were no longer of any use, then disposing of them. I think this is what he was doing with private industry. The party was a radical one and opposed to all other institutions -- schools, churches, even marriage -- that might lead anyone away from the parties goals. It is also a fact that the party leadership was corrupt and incompetent. There was no chance that they could manage a factory, and I suspect that the Hermann Goering factory was not a useful one. So the party worked with private industry because that was the only way to get the production they needed for the war. Once the party was able to develop members who could be trusted to run the factories then they would have been seized. So in that sense party was socialist. But if the workers were no longer useful they too would have been discarded. The country certainly wasn't going to be run for the benefit of workers. So perhaps not. It depends on the exact definition of socialism one uses, and future actions of the party that never came to be.