In my opinion, this is a recipe for disaster in the long run.
All passports and ID docs should ideally have current legal name. I can understand variations in spelling due to alphabet differences. Such as André vs Andre.
However, I cannot imagine country A's passport saying John Smith and coutry B's passport saying Fred Johnes.
In fact, quite a few countries, for example UK have policies for their dual citizens mandating names should match in all passports.
This is really big inconvenience from security standpoint. Dual citizens with different names in different passports should not be surprised if they're asked by authorities to explain such discrepancies when travelling internationally, for example. A person with different identities will always be a subject to additional checks by both governments.