The more I think about this I'm not sold on it. Let's discuss. Here are a few issues I've been thinking of:
We update the user profile regularly so we'd need to have an additional field we use to hold this so it doesn't get overwritten.
My biggest issue would be confusion. If your Twitch chat handle is foo but you set your name to bar, what do I call that person? Do I say "foo you're right" or "bar you're right"? I think it would be confusing for viewers (especially new viewers) to see a different name on screen than in chat.
How about allowing users in Twitch chat to customise their channel name in Fauna via a chat command?