I looked to see if there was an explanation for that one and...it's dumb.
The name "Discord" was chosen because it "sounds cool and has to do with talking", was easy to say, spell, remember, and was available for trademark and website. In addition, "Discord in the gaming community" was the problem he wished to solve.
The first part's closer to what I'd have guessed; while it is a real word with a negative meaning, it also has a similar sound to words with appropriate positive meanings like "discourse" and "discuss".
But according to that second sentence, it
was intentionally named after the word with the negative meaning, but with intent to somehow indicate the opposite of what the word means?
That's just...dumb.