I've been mulling over a web application idea and was wondering how does one go about allowing users to set up custom domains to point to their said profile/account on the application?

For example, folks can set up a custom domain or subdomain to point to their Medium account.

I haven't thought through the entire stack yet, but let's say it's either Rails hosted on Heroku or AWS using a static site set up. Is this feasible and how would one go about setting this up?

Update I've provided a crude example of what I'd hope to achieve in this comment below.