I can assure you that it is the German equivalent of the N-word in most ways, using it is frowned upon and perceived as a racial slur (although this hasn't been the case few decades below still). But people who use it nowadays are either very old or racists.

The egg in Arnolds name is probably a Styrian-Austrian dialect variation of "Eck" which translates to "corner". In Austria there are many places ending in this egg (sometimes also only with a single "g").

So his literal name might describe somebody coming from a place called "Schwarzenegg". And Schwarzenegg would be literally "Black-Corner".