Per the Matthew Stover novelization, the name "Vader" was plucked from the Force itself (emphasis mine):

Darth Sidious laid a pale hand on Anakin's brow. "Then it is done. You are now one with the Order of the Dark Lords of the Sith. From this day forward, the truth of you, my apprentice, now and forevermore, will be Darth ..."

 

A pause; a questioning in the Force - An answer, dark as the gap between galaxies - He heard Sidious say it: his new name.

 

Vader.

 

^{Revenge of the Sith: The Official Novelization Chapter 17: "The Face of the Dark"}

But there's no indication of what it means, or why the Force chose it for him.

Per the Matthew Stover novelization, the name "Vader" was plucked from the Force itself (emphasis mine):

Darth Sidious laid a pale hand on Anakin's brow. "Then it is done. You are now one with the Order of the Dark Lords of the Sith. From this day forward, the truth of you, my apprentice, now and forevermore, will be Darth ..."

A pause; a questioning in the Force - An answer, dark as the gap between galaxies - He heard Sidious say it: his new name.

Vader.

^{Revenge of the Sith: The Official Novelization Chapter 17: "The Face of the Dark"}

But there's no indication of what it means, or why the Force chose it for him.