Do you know what the conmand is to add a comment (New Comment icon on
Comments section of review tab)?
I found InsertInkComment and assigned it to Alt-c, but that didn't
work.
Is there a way to find out the command name for any ribbon icon (such
as having it displayed in the hover pop-up or the right-click list)?
Yes, there is a way to discover command names and immediately find or create a
keyboard shortcut for it.
Press Ctrl+Alt+number pad plus sign. The cursor will change into a four-leaf
clover shape. Then click on any ribbon button or press any keyboard shortcut.
The Customize Keyboard dialog will open with that specific command displayed and
ready to accept a new shortcut.
In this case, clicking the New Comment button reveals that its command is
InsertAnnotation, which has the default shortcut Ctrl+Alt+M.
Browsing in the All Commands category in the Customize Keyboard dialog also
turns up the InsertNewComment command, which apparently does the same thing as
InsertAnnotation. But this one isn't in the Review category, only in All
Commands.