On the purchase overview, you can reveal more columns if needed, which includes a “Supplier Reference” column -
This takes the value from the “Supplier Reference” field when creating/editing a purchase invoice -
“Description” refers to the item lines and searches up to the first 1,000 characters, so it isn’t necessarily the “Purchase Name”, but it could be, as this field is made up of the first 35 characters of the first line.
Hope that makes sense, but there’s more breakdown on the different fields which may help, here: Search tips - Purchases