I don’t understand why any publication, even a personal blog, would use Medium without a custom domain name. It’s not just about branding now, but about long-term sustainability. If you have your own domain name, you can keep old URLs working in perpetuity. I know many people love Medium’s editing interface, but I just can’t believe that so many writers and publications have turned toward a single centralized commercial entity as a proposed solution to what ails the publishing industry. There is tremendous strength in independence and decentralization.