Do I add Suppliers then supplier name to the category when matching a payment received in bank?

It's good to know that you're using the online banking feature in QuickBooks, info716.

There's no need to categorize or add a supplier's name to the transactions that have a match. You can directly click on Match to add them to your register. They will just use the supplier's names and categories of the matching transactions in QuickBooks.

The next step is to reconcile your transactions. Here's your reference about reconciling an account: https://intuit.me/3azMCw6

Feel free to visit us back through this thread if you have some follow up questions about handing your downloaded transactions.