Apparently, it is catching on.
Boeing mentions it is unique to 777, probably the first one to have cameras.
A feature unique to the 777-300ER and 777-300 flight deck is the
Ground Maneuver Camera System (GMCS), designed to assist the pilot in
ground maneuvering of the 777-300 with camera views of the nose gear
and main gear areas. The cameras are on the leading edge of the left
and right horizontal stabilizers and the underside of the fuselage and
are used during ground maneuvering. The images are displayed at the
Multi-Functional Display positions in the flight deck in a three-way
Boeing also has patents for this: here and here.
I am not sure if these patents prevents others to have them, because many business jets already had cameras on, and this trend is catching on even for passengers on commercials plans.
Airbus mentions this too for A340:
The A340-500 and −600 has taxi cameras to help the pilots during
I guess it has several different names, probably because of pending patents etc.
As far as the recording goes, I could not find any information.