It’s Schwarzen/egg/er, not Schwarze/negger.

A Schwarzenegger is someone from Schwarzenegg, which is a village name.

The egg root means “ridge” in old German, and is cognate to modern German Ecke meaning “corner” and to English “edge”. It’s not directly related to the English word “egg”, which is Ei in German. And it certainly has nothing to do with the Latin word meaning “black” (matching Schwarze, which means “black” and relates to English “swarthy”).

Schwarzenegg is the village named for a black ridge, or black edge.