There is some basic discrepancy in your post. A proprietorship organization is, by nature and law, the same as the proprietor himself. In view of that, even if your proprietor creates a new trade name, there is no legal distinction between them.
PAN and GST Number Concerns
In view of that, how did he get a new (separate) PAN number and GST number? A proprietor cannot get 2 PAN numbers. So you need to check that first. Either he did it without disclosing his existing PAN number (a criminal offense under the money laundering act) or he did not link his PAN to his Aadhaar, which also will cause a problem.
PF Coverage Implications
If the person is the same (different PAN number notwithstanding), he is liable to be covered under PF as one entity, and they will never accept that he has done it for genuine purposes. If, on the other hand, the actual constitution is different from what you think, you can use that to resolve the problem with the PF department.
Consideration for LLP Conversion
In the meanwhile, it may make sense for your boss to convert his entities into separate LLPs, which have different partners to prevent this problem.