Selected CSYS in part (or assembly) should always have the same name as part (or assembly), even after renaming the part (or assembly).
After RMB on CSYS, there should be the option to turn this on/off, or at least it should be possible to make this happen with relations (renaming CSYS with relation).
Currently, there is only guide from PTC how to make this with PRO/Toolkit, which not everybody has (me either).