If a business has copyrights on their products listed on their website and the product is made by a different company, can I use the same name for that product?
The name is presumably copyrighted, assuming it is not a purely descriptive or common name which cannot be protected by copyright. Similarly, there is a good chance it is protected by trademark law, if the name is again not generic or descriptive. (E.g. "Mustang" can be protected as a car name; "sports car" cannot be, because it is a common descriptor, not original and not distinctive.) You are much better off coming up with your own name for the product.