Need help renaming a Legal Entity under Manage Legal Entity HCM Information

Summary: We have a case where we renamed a Legal Entity from X to Y to remove the periods (RIA Italia S.R.L. to RIA Italia SRL). Although the name has been updated under the section "Manage Legal Entity HCM Information" to RIA Italia SRL, it does not flow down automatically to the employee profile Employment Section. It is still appearing as RIA Italia S.R.L. Is there a scheduled process we have to run, in order for the name change to automatically flow down to the Employment profiles?

Note that we did not date track. We simply overwrote the existing legal entity name, Saved and Closed. This is needed in order to complete a mapping integration with another internal system.