Well, your domain, not a "subdomain" would come from a domain register like Name Silo or Name Cheap, etc. I would never use my host as the register for security reasons. I use Name Silo and they are pretty good. You won't get a free domain. That you have to pay for. It's about $10 American a year.
With free hosters they really aren't that good. As they say you get what you pay for. I've used this service before.
https://x10hosting.com/ It was alright, but PHP mail doesn't work. If your site is PHP driven that could be a problem.