You need a trendier, buzzier name for it, and perhaps a three-letter acronym. "Inbox of Things" (IoT) should work to gladwellize the minions and get people talking.
But since the chatterati think email is the spawn of old white european males, you need to get rid of "Inbox" all together. Way too emailesque.
Also, we live in the most narcissistic, shallow society ever to have sat idly on this good planet earth, so you need some combination of self, selfie, me, my, myself, you, etc.
Of course, in the selfie-sphere the major issue you will face is appearing "needy" if you respond to pings quickly or respond in a personal, non-selfish way. The proper form of communication in narcissistic society is merely post inane self-expressions in hopes of garnering hip-metrics of reblogs, retweets, likes, upvotes, and other simplistic pings.
So what you really need is an one-way orifice for self-expression that merely reports social metrics back in gamified form. Sort of like a toilet with an AI success coach built in.
The flushing metaphor has its limtis, because "flushing" makes it seem like you don't care about water conservation and other hip non-selfish, selfish things that aid your image-crafting. An "air flush" would solve the water conservation issues. So what sound would an "air flush" make? A swish, a blow? That's it.
So we should call a universal inbox in the selfie age? How about: "Blow Me"