The name “Darth Vader” was given to the character well before it was ever determined by George Lucas or any of the other writers involved that he would be Luke Skywalkers father. You’re looking into that one a bit too much (like many others) when the reality is the name was chosen because it was ominous sounding and evoked the concept of a dark religious symbol, an anti-christ of the Empire if you will.

Curiously, the name connection you did miss is that of Palpatine, which is derived from the latin word “Palatinus” or more commonly “Palatine” which was the term used for certain high-level government officials in Roman and later European royal/imperial courts, and in some cases used to refer to an emperor/king or the palace itself.