You can create new/rename Patient/Study/Series in Data module in Subject hierarchy tab. When the study is completed you can export it to DICOM. If you enable import option then the exported study will be automatically imported into the DICOM database.
You can create new patient/study/series in the DICOM database by creating a DICOM dataset in memory or file and using it as input for ctkDICOMDatabase::insert().
DICOM standard does not allow you to modify any details of an instance after it is created, as the standard heavily relies on unique identifiers unambiguously identifying a complete data set. If you must modify data then you have to delete the original data set from the database and re-insert a new instance. If there is a chance that the original data set was exported from Slicer to external systems then you must generate a new UID (PACS behavior is undefined if it encounters modified data sets with the same UID).