Yeah, I'm sure there's a reason why they adopted that name but, considering how many people the Nazi Party exterminated solely on the grounds of their Leftist sympathies, it does seem very odd.
EDIT: I just looked it up and it seems that the Nazi's opposed any non-national brand of politics, regardless of whether it was of the Left or the Right. I'm assuming that they opposed Soviet Communism because of its underlying 'internationalism'. Furthermore, according to
this site the word was used "to appeal to German workers for political support during the tentative early years of Hitler's ascent to power. Apart from the occasional use of empty pro-worker political rhetoric, Adolf Hitler and his Nazi party had no inclination towards true socialism."
Edit 2: In terms of a difference between the Left and the Right, I've always assumed that the Right places a far great emphasis on the rights of the individual and as such believes in the idea of minimising government controls (except those involving the military and the police) while the Left has tended towards more community based policies with a far greater belief in 'bigger' government. When either of these become dictatorships though, the boundaries seem to blur a lot more. As seems to be the case when either tendency morphs into things like Anarchism or Libertarianism.