Register live streaming business?

I would like to stream on Twitch but first of all without making any money, i.e. Without a donation link or the opportunity to subscribe. Do I still have to register a trade? According to the Internet, only if I intend to earn money and I don't.

You don't need a business there. You can only subscribe if you are an affiliate. And even then you don't have to register a business. That comes much, much later.

There's no business without profit making. So no.