BYO Domain?

This really depends on too many variables to provide a pin-point answer, like, where do you host the service, or, what's your Internet-facing webserver?

When you're using Apache or nginx as a webserver, you could accept requests from all subdomains and proxy the request to your backend, but add the extracted subdomain as a header. Then, you could parse this header in your backend (using a middleware/filter) and determine your user accordingly.

Here's a corresponding nginx example (via Reddit):

http { 
      server {
           server_name ~^(?<subdomain>.*)\.example\.com$;
           proxy_set_header X-Subdomain $subdomain;
      }
 }