Some terms…
my_domain.org is a domain. That’s what you register with an isp.
www.my_domain.org is a subdomain and you can (probably) create whatever of those you want if your isp allows it.
For anyone to find that domain and subdomains, they need a dns record. Those come in many flavours. Two flavours are A records and CNAME records.
A records map a domain or subdomain to an ip address.
CNAME records act like aliases. If a subdomain needs to point at the same ip address as another subdomain, you might create one A record and then use CNAME records for the others. That way, you o ly have to change one record if the address changes.
You could use multiple A records mapping to the same address and it will work fine. It’s just more effort if the address changes.
Many domains set an A record at the domain level pointing to a Web server and create a www subdomain with a CNAME record. That way, users typing either in their browser end up at the same website.
SSL certificates are choosy about what domains and subdomains they are valid for and they treat the two as separate beings.
It’s possible that a certificate will handle both levels but you ha e to explicitly define that when you create the certificate. By default, they often only handle one.
So, your certificate needs to match precisely the subdomains you type into your browser. Even if you correctly use A and CNAME records to map multiple domains and subdomains to the correct address, your certificate might only be valid for one of those.