Item Name/Number is the unique primary key identifier for Item Records. The system will allow users to enter the same Item Name/Number provided that they are of different Item Types. A Matrix Item is an extension of a standard Item Type and by design is treated the same way as its parent type, i.e. Non-Inventory Matrix Item is still Non-Inventory while Serialized Matrix Item is still Serialized Inventory.
To illustrate, if there is a Serialized Inventory Item with Item Name = AAA then the same name can be used to a Non-Serialized Inventory Item. However, creating a new Serialized Inventory Matrix Item with the same name will return the error message 'There is already an item with that name.'
The solution is to edit the Item Name/Number of the Serialized Inventory Matrix Item by adding new character(s) before saving it.