First of all there is no change in accounting, credit control or any others, changes is, SAP display the new customer name in all entry screen or documents, either it is old document (before change name) or new document which is created after change.
SAP maintain only change log but here is no effect from to date filtration.
In concern of customer name SAP looks customer code for any document.
Table: ADRC Fields are NAME1, NAM2
Table: KNA1 fields are NAME1, NAM2