The developers of Discord respond this way:
Jason: We picked the name because at the end of the day it just sounds cool and has to do with talking. We had a bunch of names that we bounced around, but picking a name for a product is a complicated process. You want a name that is easy to say, spell, remember, related to the function of the product, available for ™, and has a website you can get. There are a lot of things to consider and we had a number of different candidates. Discord met all the criteria that we had and we fell in love with the name.
Socrates: And Discord in the gaming community is the problem we are trying to solve with this product.
Answer #2:
Discord was originally created as a way for gamers to communicate with each other while playing online. The name Discord was chosen to reflect the idea of bringing people together in a virtual space to talk and share ideas. The name also reflects the idea of discord, or disagreement, which can be a part of any conversation.
Answer #3:
What he said! It’s a little contradictory seeing as Discord means “many chaotic noises or voices” but we like to shoehorn that into “bringing many cacophonous noise into one harmonious voice”. It’s a stretch, but that’s what I’ve got. =]