I may be missing something, but I haven't seen an area where you can map a chosen ID field when importing Origins and Destinations. The Name property is the only kind of field where this mapping is possible, but then the Origin and Destination data is concatenated together in one field.
It would be preferred to be able to map an ID field that is concatenated together like the Name property, but also split up into their own OriginID and DestinationID fields...almost like building a junction table right into the output to take advantage of in post analysis operations. It's not too hard to map ID fields to the Name property and do some string manipulation to split out the information, but seems kind of surprising this isn't an option. It seems like a typical operation after conducting an OD Cost Matrix would be to join it back to the original data in some way to populate attributes or conduct additional analysis.