So when you talk about naming a pattern, there seem to consistently be 2 elements to a pattern's name. One is the item being patterned, the other is its behavior/action. So for example, 'inline edit' tells us that we are editing a field, and the behavior for editing is 'inline' (versus click to edit, etc). Common terms seem to be 'inline', 'hover', 'continuous', 'dynamic', 'prompt', 'spotlight', 'drag-and-drop', 'modal', etc.
In this case, we've got something that is appearing based on triggers--location on page, time on page, distance scrolled to bottom (say 70% to bottom of page), etc. And it's appearing and sticking, or appearing and fading, depending on the implementation.
One term I've seen for SIMILAR functionality is 'Toast Notification'. http://bit.ly/spg3yr and http://bit.ly/st3OLL.
I think it fits your need--it tells us what is happening: "Toast", i.e. something is popping up at a pre-determined time (when the toast is ready!). It tells us what is showing up--"Notification".
Another term that might be application instead of Notification is 'Call to Action'. So you could consider it a Toast Call to Action. In this case you're wanting the user to do something--click through to a new article, provide feedback, rate an app, whatever.
In terms of usability--the concept is already prominent within OSX and Windows. Growl notifications, system tray notifications, etc. are all forms of this same type of behavior. Tell the user something happened in a conspicuous manner, outside of the scope of their working interface, and allow them to act on it. I'm willing to bet at least some of the folks above who are poo-pooing it also use OSX with growl enabled. I'm not bashing!, just trying to point out it's a little more ubiquitous than we might think.
So, call it a Toast Notification or Toast Call to Action. Use it when you want to conspicuously inform the user of something, outside of the 'frame' or 'scope' of their working interface/reading area, and allow them to take action on it--including closing it, clicking through, whatever.
Hope this helps!