Facebook don't really embrace the idea of an alternate persona, in fact it's almost antithetical to them. Interesting to watch this play out.
I'm sure it might be possible to figure out which facebook real name made and owns that page. But at face value I was able to stream and comment under my alternate persona. namrog84. Without having to make a new Facebook account. They have a drop down in streamer chat if you want to use your real name or a name of a page.
With that said, I'm very hesitant of fb gaming streaming and this is my first ever time really looking at it.
The first LPT I taught me daughters when they started using the internet is that on the internet, you are a super hero - no one should know your real name.
I don't have children, and as a 20-something I know the struggle and seeming impossibility of avoiding FB products, but I try to avoid pouring my whole identity into them. It's rough when the social culture is rapidly shifting to "unless you put everything online you're not worth my time" or makes you one of those "privacy nuts."
Once you start connecting, you unmask yourself quite easily - many have tried creating spare accounts (even with VPNs and separate browser contexts) and have quite quickly been shown their exist friend set as "recommendations by FB".
Look at all the dumb things people say with their real names on Twitter as well.
Discussion is civil when you actually cultivate civil discussion, not when you force people to use real names.