Well they’re off to a good start if they want Azure to dominate the industry. First Xbox Live, now PSN. However, this is just a branding move and it makes sense since GamePass will soon be out of beta on PC and available with xCloud as well. GamePass on my tablet or phone is more natural than Xbox GamePass on my tablet or phone, having the Xbox name in there makes it seem as if I need an Xbox or is tied to my Xbox.
They’ve always said local hardware is the best way to play games and streaming is ten+ years off. If that’s “next gen” then this will be quite a long gen.