It happened all the time, not necessarily in MNF-West all the time, but throughout the whole country, General Johnson testified, using a military abbreviation for allied forces in western Iraq.
Does MNF-West mean western multi-national forces?
I would interpret it differently:
MNF = Multi-national force
West = the area of Iraq they operated in, so there would probably be a MNF-East too.
I doubt very much that they would use Western for a foreign military force in the Middle East- it would be very controversial.