Sometimes the names are called differently by you and your customers. To record it, control it and print it on external documents, you may need to define the customer item and map it to your own item number. The definition/setup path is Inventory > Items>Customer Items. The customer item can be set up at three different level.
“None” Level – The top level. You can use this customer item for any customer’s order, sometime it is like an item’s alternative name.
“Customer” Level – You can only use this customer item number for this customer’s order. You need to specify the customer when you create customer item.
“Customer Address” Level – You can only use this customer item number for the orders which under the specified customer address.
Above three level setup could be able to fulfill your requirement to control the item utility. But if you hope to show different names against different situation on your external documents, you may need to set up/customize your own report.