Creating new s corp name or retaining old name

I currently have a s corp for my website design firm and I plan to operate another business that sells food and groceries online. Am I better off creating a new corporation or using my old corporate name? Any pros and cons of doing one or the other? Eventually, i plan to close my s corp for web design because business is slow but I get a different answers from people. Some say it is better using a old corporate name because it has longer corporate history but I never borrow any money and others say it is better to start fresh with less confusion since we will have different shareholders. What do you guys think?