I don't think Nazism is considered a form of Socialism by pretty much any reputable source; only some in the anti-Left fringe do. A planned economy alone is not enough to classify a system as socialist, and anyway Nazism had enough elements of private property and corporatism. The Nazis, like in many other aspects, were equivocating by calling themselves socialists -- not that they particularly liked the term themselves very much.
I wouldn't pay much attention to the name of the Nazi Party, either. After all, North Korea is a "democratic" republic, it says so right in their name!
So if a command economy isn't enough, perhaps it has to actually represent a form of community control, do you believe the USSR was any more socialist? What makes something actually socialist?
The understanding I've developed of socialism is of worker ownership of the means of production. The state at best can only claim to somehow speak for the workers in a top down manner, and I think that inevitably fails. (Which is not to say I'm advocating it here in a decentralized form but I'm much more sympathetic)
I wouldn't pay much attention to the name of the Nazi Party, either. After all, North Korea is a "democratic" republic, it says so right in their name!