Does a subdomain have to be registered like a regular domain name?
Nope. A subdomain is just another part of the main domain. Once you have registered “yourdoimain.tld”, you are then, by default, the “registered” party for all the subdomains associated with it (www.yourdomain.tld", blog.yourdomain.ltd, gallery.yourdomain.ltd, bill.yourdomain.ltd, etc.)
And, for that matter, even multiple levels like sub1.sub2.sub3.yourdomain.tld. DNS is hierarchical.