Why are you using the product name as the name of the text field? What type of data are they entering into the text field? Is this the quantity box? If so, I would change the name of the field to something like qty[$Row['productid']] (where $Row['productid'] is some unique identifier for the row, such as an AUTO_INCREMENT column). Then, when you process the POST'ed data, $_POST['qty'] will be an array where the keys are the product ID's and the values are the associated quantities that the customer entered.
As for storing the order, you could break it down into three tables: customers, orders, order_items. Table "customers" contains personal info about the customer (name, address, etc. etc.). Table "orders" contains an order id and any other metadata you might want to know about the order (datetime ordered, datetime shipped, shipping reference/tracking number, etc. etc.). Table "order_items" would contain an order id, product id, quantity, and any other information you want to store (e.g. price per item (which could change as you adjust prices), adjusted/discount amount, etc.).
Obviously the above DB schema is just some generic example I created on-the-fly... your specific needs might warrant additions or omissions from the basic structure.