You have correctly created the mapping table. The particular way you are using the mapping table:
Rename FIELDS USING MAPPINGTABLE
will rename field names, it does not change field contents.
If you want to change the contents (values) of a field, use either the MAP statement or the ApplyMap function.
For example, to change the map value in the Customer field:
MAP Customer USING MAPPINGTABLE;
Place the MAP statement in the script before the Customer table is loaded.
To map values as they are loaded, use the ApplyMap() function in a load statement.
ApplyMap('MAPPINGTABLE', Customer) as Customer