What is the name of the program that is invoked when Alt+F2 is pressed, in Gnome?
The grey dialog box presented here, where you can type in the command/program you want to run:
from this article on the Alt+F2 shortcut; what is the name of the executable file that runs this?
It is not a separate program. It is a part of Gnome Shell, not quite consistently referred to as the "command dialog" or the "Alt+F2 prompt" in the official Gnome Shell documentation.
The javascript code for that part of Gnome Shell can be seen here (Thanks to user Raffa for providing the link).