I'm trying to clean up notifications for a client site and was wondering if the notification pattern that Stack Exchange employs has a name that I can use to search for more examples.
The terms I see the most are "message bar", "notify bar" and "notification bar".
There are tons of examples with Google using the terms above. Below are a few.
Within Google, we call it a Butter Bar, to disambiguate it from all the other types of notifications that might also be shown on a page.
I just found a good page from Chromium project about this UI element. They call it infobar and have there quite nice guidelines, rationale and examples: http://www.chromium.org/user-experience/infobars
IE calls it "information bar".
It's called banner in material design: https://material.io/design/components/banners.html