Can I use a name brand ketchup in my home made barbeque sauce and sell it?

You can use anything you want in your sauce. You will need to know the contents of whatever ketchup you use in order to include the ingredients on the label of your sauce.

When someone buys a product, even a name brand product, they can generally use it in something that they create without getting permission from the original owner because the purchase includes implied rights.

You certainly want your new product to be made from the best ingredients available. Generally, food recipes are quite difficult to patent. Even if the ketchup name brand was patented, you are buying the product and as a purchaser for value, you have acquired a license to use the product for the purpose that it was made to add flavor. You will need to list the ingredients of the ketchup in your barbeque sauce. If you are successful, the ketchup manufacturer will be selling you a lot of product, and so it's a win-win. You need not list the brand name of the ketchup on your barbeque sauce. And, certainly, you are not infringing any trademark if you make no reference to the brand name of the ketchup. This is but an informal opinion and you would be well-advised to seek the advise of counsel and good luck!

Once you purchase the ketchup - you are free to use it. However - you are NOT free to use the brand name without permission of the owner. So your ingredient list would simply include the generic term - ketchup.