He was an experimental clone of Palpatine created by a Sith cult. Sort of a Frankenstein’s monster, as he was an earlier experiment.
Rey’s dad (Dathan) was another clone, though a much more subtle one; he was a hybrid of sorts and didn’t inherit any Force abilities (they manifested in Rey instead).
The clones were called “strandcasts” and made through Sith alchemy rather than the science that Kamino used to make their clones. The results were a lot less predictable.
Wait, was all of that in the movie?
Some of it was, certainly not all of it.
We’re to the point now with SW lore that the movies showed not even 10% of what Lucasfilm’s “official story” was. The rest they dribbled out in various “about” books and in expanded commentary on DVDs, etc. And as noted above, the whole thing wasn’t planned; it mostly was invented as they went along, retconning to paper over some of the worst of the cracks.
Then there’s the non-canonical fanfic & websites and … which outweighs the “official story” maybe 100 to 1.
I think “sith” might have been on the action-figure packaging, too. That’s where a lot of Star Wars lore originates.
I’ve always been extremely skeptical of the “Dark Father” thing. When the name “Darth Vader” first shows up, in the earliest drafts, it was applied to a fairly minor Imperial officer, not any kind of Force-wielder, not the major villain, and certainly not likely to be the hero’s secret father. I think it was just a name that sounded cool, and as Lucas was writing and re-writing it eventually made it to the main evil henchman.
Yes, henchman. That’s clearly what Vader was in the first movie. Tarkin was in charge of the Death Star and all of the Imperial forces that we see. Vader was there to be intimidating, to do some hands-on fighting when needed, and to Force-choke random annoying guys during committee meetings.
Pretty much that. Star Wars is full of retcons, and Vader’s role is one of them. He ended up being so popular with fans that Lucas retconned his role to be much more important. And that includes his name, which became a title instead.
Boba Fett got similar treatment when he got popular outside the direct context of the movies.
Man, don’t get me started on Boba Fett! 
Agreed; I think Lucas made up that story after the fact.
Still, that’s the most “official” explanation that is out there as far as I know.
I mean, “Darth Vader” obviously comes from “Dark” and “Invader”; just as later on, “Darth Sidious” came from “Dark” and “Insidious”. George Lucas has never been accused of being subtle.
Boba Fett? Boba Fett? Where?
[turns around and knocks Boba into the Sarlaac pit]
Yes, that’s another theory, and I think that George may have been quoted in saying as much. It’s really a big mess as to what is true and what is BS made up to sound good.
Another factoid… George went to high school with another kid named Gary Vader, who was a football player one year older than him. He acknowledges that it might have subconsciously influenced that name choice, though he insists it wasn’t intentional.
(In my headcanon, Vader’s real name is Gary, and he has secretly murdered everyone who has ever possessed that knowledge to preserve that secret. Because nobody would be afraid of Gary, Dark Lord of the Sith.)
Goes a long way to explaining why Gary Darth is so comfortable wearing a helmet. Some people peak in high school.
I thought you, of all people, would point out that Obi-Wan does call Vader “Darth” (“You can’t win, Darth.”)
In my head it was “Garth”, and he got tired of being introduced by Obi-Wayne-a, his Jedi master, with “and with me as always is Garth.” So he used his skills to make the baddest-assed light saber ever, and killed all the Jedi. And then he started calling himself “Dark Garth”, or more easily, Darth, as he came to be known.
Party on, Darth!