It isn't wrong - it's just how Odoo is designed.  

Odoo stores the name of the product, so you can differentiate between Sales and Invoices of the 'old' product if the name ever changes.

name stores the name of the product as is was when it was added to the Invoice.

A possible scenario that resulted in what you are seeing:

1. User creates product zzz (copy) by copying product zzz.

2. User adds product zzz (copy) to an Invoice

3. User renames product zzz (copy) to something else.

If you look at product_id you will find the id of the product.product (which will still be in the database).

Of course does the product exist in the database. Please check the translation values. This happens when duplicating objects while having more than 1 language active.

Example:

You have a database with 2 active languages, french and english. Now you have a product with the name "Product A" and its french translation "Produit A". A user with language preference french now duplicates this product, he sees "Produit A (copy)" and changes the name to "Produit B". But the english name of the duplicated product is "Product A (copy)", if you do not translate it, then this is the name which will be shown to english users through the whole system.