What is the official name for this icon/button? What is the official name for this button/icon: 



It's found in many places throughout Blender: 

 

I can't find it anywhere in the manual.

If you know, can you please cite the source for your information (i.e. a page from the Blender Manual) because I'd like to read about it.

Thanks!
Andrew Price called it "Dot Symbol" button:

http://youtu.be/xYiiD-p2q80?t=8m58s

I would call the particular ones you show "Node Material Properties Dropdown Buttons" to be honest. I'm not sure why a differnet icon is used here, using a symbol not "universaly understood" like Andrew said.