Cascade update doesn't update data fields, it ONLY updates foreign key fields. If your Customer table contains the primary key CustID and the Order table contains CustID and a relationship has been defined between the two tables on the CustID field, the CustID field in the Order table becomes a "foreign" key. If you change a CustID in the Customer table from ABC to ABX, the foreign key values in the related records of the Order table will be changed from ABC to ABX in order to maintain the relationship.
Given this same db structure, if you duplicated the CustomerName field in the Order table, it would not be automatically changed when you change the value of a CustomerName in the customer table. This duplication would violate second normal form and therefore, there would be no built in tool to help you. The solution is to remove the CustomerName from the Order table. Whenever you want to display an Order with the relevant Customer information, use a query that joins the Order table to the Customer table on CustID. That will make available to your form or report, ALL columns from both tables.