From the Medium Help Center:
Medium is no longer offering new custom domains as a feature. If you already have a custom domain on Medium, nothing will change for you for the foreseeable future, and your domain will continue to work as expected.
As best I can tell, this decision is a change from January (courtesy of the Internet Archive), when the help page for custom domains read that Medium was “pausing” offering the service. It would now seem they don’t offer the setting at all.
I wonder if current custom domain users find the “for the foreseeable future” bit at all reassuring. I wouldn’t. Using your own domain was one of the few meaningful ways you could separate your Medium-hosted blog from all the others. Anyone signing up today will be stuck using whatever publication names (
medium.com/publication) are still available to register, making Medium more akin to a long-form Twitter than a place to keep a blog. Lame.