The process of naming a Sith lord often varies from being a short to a long process. In the case of Darth Vader, Palpatine looked through the dark side of the force, in a sort of quick meditation, and was inspired the name "Vader" for his apprentice. Though a case like that rarely happens. The normal way of Sith naming requires an apprentice to extensively prove him/herself to the master, once this happens the master will give the Sith title to the apprentice. It is speculated that Sith title names are words from the ancient Sith language, words like "deadly", "haunt", or "death".
Another interesting fact is that Vader is also Dutch for father.