To change a BidTable Basket Name, first select Actions -> Edit from the BidTables section of the Project Details page:
This will take you into the BidTable. Select Edit Baskets from the Actions drop-down:
This will open up a menu with all of your Baskets. In the Edit Baskets window double click the basket number in the # column. That BidTable Basket will reassign the order accordingly. Press Enter on your keyboard or click on another box to save the changes.
When you are done, click Hide at the bottom to return to the previous menu.