https://www.polygon.com/2018/1/9/16868566/xbox-live-dnd-do-not-disturb-appear-offline

Your Xbox will eventually get a virtual “do not disturb” sign when a feature coming to the Xbox Insider program makes it to everyone’s systems. The option will allow you to play online while also showing friends and other people on Xbox Live that you’re not accepting messages nor interested in any other games.

“Sometimes all you want to do is avoid all distractions and focus entirely on your game,” the official post states. “We’ll be including a ‘Do not disturb’ online status, which will suppress notifications and let your friends know that you’re not available for another game or activity right now.”