I first joined the first two sets on Region, and then the last on Product group, using the last join tool to both drop the extra column from the right input, and change the data types of the two codes to be strings.
I then simply created a column using the formula tool which creates the file name ("Region"+[Region Key]+"_"+"Product"+[Product Key]).
I then created the output to .csv, and configured the output as follows:
NOTE: Check the "Take File/Table Name From Field" and select the Identifier field as created in the previous step. Un-check the "Keep Field In Output" box, which will drop that column from the data.