I don't think configurations within the multi-body part file will do you any good, it will show it's file name or part number though the configuration or individual part body name may be shown as well. You may need to keep or reserve the master multi-body file as this. Add a save bodies feature which creates a new part file for each selected body. The part files would be treated as a normal part file for an assembly, BOM, and such. You would need to name the master multi-body part file in a way that makes sense to you and works for your needs.
Another option, once the design is completed for the master multi-body part file, is to create copies of this file each with their own part number file name. Delete the bodies in each part file until only one is left present, different for each part #. If revisions are required later on, you can just add features to the part file to do so. No master part file is driving other parts, assembly, BOM, and such works just fine, the bad is large file sizes and speed due to being redundant in the software resolving the same things over a number of times only for that to be deleted.