Studies belonging to different patients should have corresponding unique patient identifiers. If the sending systems are not ensuring unique patient identifiers, you can create a coercion rule to add an IssuerOfPatientID on receive of studies.
Create an Archive Attribute Coercion (Available at Menu -> Configuration page -> Devices tab -> dcm4chee-arc -> Device Extension -> Archive Device Extension -> Child Objects -> Archive Attribute Coercion) and set Merge Attribute as for eg., IssuerOfPatientID={PatientName,hash}-{PatientBirthDate}. (You may choose to use any attribute from DICOM dataset). Set DIMSE as C_STORE_RQ and DICOM Transfer Role as SCU. Configuring this rule will ensure that patient identifiers are unique when studies are stored to the archive.