MS's branding is so ass, they really need to consolidate down anyway. They're not even opposed to reusing branding for completely different products and retroactively renaming old products.
Example being the Surface brand was originally a touchscreen windows 8 table top for ordering shit in restraunts. Or playing games on. Nevermind the tablet stations bolted to McDonald's tables these days. Then it was for defining new tech category times. The tablet with a breakaway keyboard, the double screen Duo phone, trying to do something with headphones and buds markets.
Live was used in everything from Windows Live Search (Bing), Internet focused feature pack suite naming (Windows Live Messenger, WL Movie Maker, WL Blogger etc)
They have (direct)x...box, referring to a console device, when they seem to be trying to transform into a service everywhere under the GamePass banner. Then there's XboxCloudGaming and such mucking up the gaming convo as well, not even going into MS side with like MS365 etc.
I think they should leave Live branding to a bygone era, try and absorbe the GP branding back towards XB (stupid move to create a split into PC Game Pass imo), but try to split features offered between an XBGame Pass and a XBCloud Pass. Perhaps XBGP sub allows you to DL games to XB console, but only the XB Cloud Pass allows you wider range of games to stream?
At that point it's all semantics anyway, Office 365 became MS365, but always offered a pack-in of OneDrive storage. And I'm fairly sure every sub division like Office and XB are literally filed under the Azure/Azure Cloud borg to make that look like the hottest shit.