As of November 2017, Medium is no longer offering new custom domains as a feature. Instead, you can create a publication on Medium that will live on a medium.com/publication-name URL.
I don’t know why anyone would invest time and energy into a publishing platform that doesn’t support custom domain names. If you want to start writing for the web, do yourself a favor and just go with WordPress. Whether it be self-hosted or through WordPress.com, there will come a time when you will greatly appreciate the flexibility and portability offered by the platform.
(Via Daring Fireball.)