According to George Lucas' retcon Rolling Stone interview in 2005:
How did you get the name Darth Vader?
"Darth" is a variation of dark. And "Vader" is a variation of father. So it's basically Dark Father. All the names have history, but sometimes I make mistakes -- Luke was originally going to be called Luke Starkiller, but then I realized that wasn't appropriate for the character. It was appropriate for Anakin, but not his son. I said, "Wait, we can't weigh this down too much -- he's the one that redeems him."
Now, there are reasons to suspect that wasn't necessarily the case originally:
In A New Hope, Obi-Wan Kenobi addresses Darth Vader simply as "Darth". That sounds like a proper name, not a title.
There are persistent rumors that Vader was from "invader". I was never able to find a firm proof of the link, but sounds plausible. LukasLucas DID the same thing with Sidious, after all.
There are reasons to believe that the "father" angle was developed way after the name. From "The Visual Development of Darth Vader"
In the first draft, Darth Vader is fairly inconsequential, and is merely an Imperial General; most of his later traits are exhibited instead by Prince Valorum, a Sith Lord who dresses in black robes and who speaks in terse, no-nonesense phrases. Both of these characters are human and generally unremarkable in the visual sense; no artwork was ever done. In draft two, however, the two characters were combined, and this is where the Darth Vader that we are familiar with first becomes recognizable in prototype form.