First, all the Eaton brands should be set with the "Parent Company" entry of "Eaton" (or related entry in your system). Merge brands should only be checked if the orders for that brand may be combined on one Eaton order.
The reason for having the OASIS "Eaton" entry as a parent of the brands in OASIS is to allow the customer numbers to be keyed once - on the Eaton manufacturer in OASIS - and not for all Eaton brands (that would be a lot of work).
First, open the Eaton entry in OASIS. Once open, select "Show Customers" from the "Cooper" menu at the top of the screen:
This will take a minute to run, but a report will be generated showing all your Eaton customers and the related customer codes in pdf format. Print this document and use it to manually enter the codes to the Accounts tab of the Eaton manufacturer entry in OASIS:
Use the icons to add and remove customers from the accounts tab. For each customer, key the corresponding Eaton account code.