That should work just fine, it doesn’t matter if the domains are different or belong to different companies. As long as the subdomain points to your application domain, using a CNAME DNS record, it will work.
You can stick a haproxy server in front of your app. It can listen on many ports and IPs and SSL certs and funnel all the traffic to your app on one IP/port. It can add a HTTP header for your app to tell which connection it is. See https://www.haproxy.org/ for more info.
thank you all for these constructive responses.
I mark Ricardo as the solution, but everyone has a good answer.
I will experiment all of these and report here the choosen one !