CustomerOrder domain model has a properties EmployeeId and EmployeeName you may use it to store information about order responsible.
VC expose multiple extension points and one of them is a Events http://docs.virtocommerce.com/display/vc2devguide/Extending+using+events. In you custom module you should subscribe to OrderChange event
//Subscribe to cart changes. Register in avalara SalesInvoice transaction
_container.RegisterType<IObserver<OrderChangeEvent>, OrderTaxAdjustmentObserver>("PlacedOrderObserver");
And inside you event handler implement order responsible assignment logic.
To implement auto-assignment functionality you should create new
module (any of VС extension should be only in custom modules to
preventing merging hell on updates)
Concerning to assigned to UI and filtration we added issue in github https://github.com/VirtoCommerce/vc-platform/issues/559 because it is the overall order functionality and it should included in Order.Module and should be realized our team.