You can shake and strain this over ice if you want to blend the ingredients fully. I prefer to have the vodka and Kahlua swimming around partially blended. I get some sweeter, more coffee flavored sips interspaced with some stronger, drier sips from the vodka. The interplay is interesting to me. Eventually as the ice melts, it blends together more thoroughly by itself.
A Black Russian is not a Russian cocktail. It was invented by Gustave Tops, a bartender at the Hotel Metropole in Brussels, Belgium in 1949. This was a time when the Cold War was just starting and the euphoria and relief at the end of World War II was a distant memory.
In 1949, vodka was associated with Russia (this is before Absolut). This combined with the ominous clouds of the nascent Cold War gave the Black Russian its name--it also helped that the drink is very dark in color.
Gustave Tops made this drink for his friends, and is reputed to have made it for the U.S. ambassador to Luxembourg. Since then, it has become one of the most popular coffee liqueur based drinks along with its White Russian cousin.