You can run your own mail servers no problem. Takes about 15 minutes to get going at its simplest level. Now, there’s a whole bunch of problems you’ll run into as soon as you open it to the internet, but that’s a separate topic.

If you just want to use a custom domain: register any domain, find mail host that supports custom domains most do with a paid subscription), and setup your DNS records to point to wherever that service is. No you have mail coming to “beepbopboop@whateverdomainyouregistered.com”