Sound like data grid of orders with
[Order_Customer/Customer/User_Customer/User = '[%CurrentUser%]']
but i guess you already tried that?
After update 1:
So you need to compare the names, but the name is an object which is associated to the user? Thus you would like to retrieve:
[Order_Customer/Customer/Name = '[%CurrentUser%]'/Responsible_Customers/Name]
That is not possible currently. As you already suggested, you need to maintain an association.