How to change name from sub-server to SUBDOMAIN and virtual server to DOMAIN?

You can edit it by going to the sub-server (or sub-domain) account in virtualmin and then finding: server configuration > change domain name

Then you can change the domain name. Also note that you have an option to keep the folder name same as old one or you want to change it too.

Very interesting as long as you do understand that all bugs are insects - but not all insects are bugs.

Do you understand what the DNS server sees? If you do, then you may ask your DNS provider to approve what you have in mind. I am a DNS provider, and I can tell you the rest of the internet is in agreement about stuff you might not understand. About so many non-conventional things:

Mapping IP addresses (mapping is the key word) is the primary purpose of DNS, such as google.com responds with 100+ IP addresses or www.google.com is mapped to ONE IP address... Never perfect of course, security considerations make the simple fact of mapping IP addresses into a warfare of digital encryption service... so on so on..

The BEST way to FIX any DNS problem is to run your own DNS server. See what the rest of the internet think about your work! Chances are you are going to change your mind and realize the internet is fine...

It is possible the OP do not understand the purpose of glue records.

But for the sake of argument - I agree with the OP in regards of transparency,

For example, when I connect a new Virtualmin (VM) client to an existing Cloudmin (CM) "DOMAIN" cloudmin.mydomain.tld ... I have LDAP configured, so for the OWNER(s) of the VM I use local, but for all other users created on DOMAINS and ALIAS and SUB-DOMAINS by OWNER(s) I use LDAP because Webmin is configured so..

This is where LDAP really, really shines.. I map all newly created "DOMAIN" Webmin to cloudmin.mydomain.tld - but then I configure every so-called "DOMAINS" to authenticate to domainABC.cloudmin.mydomain.tld. Or, if I have tenants who want their unique domains I create the new tree and new credentials and map to that (such as tenantABC.tld).

Once LDAP access is configured in the Webmin modules - Webmin creates these new entries anywhere under dc=mydomain,dc=tld. For example when I have a tenant called "ABC PLANKS" I can add abc_planks.mydomain.tld - and Webmin is going to ask me if I really want to create dc=abc_planks,dc=mydomain,dc=tld.

So the question is: you want to create your DNS or your LDAP first? I would say DNS every time, especially because you might want to put two LDAP servers in place called ldap-sid1.yourdomain.tld and ldap-sid2.yourdomain.tld and these are FQDN..

From the OPs point of view.. If you are able to fit the hierarchy you should be able to see what is a server, alias, sub-server or whatever you name and concerned with. Of course it WOULD help greatly if we all used the same dictionary and call things in a standard way. I doubt this is ever going to be a practical argument though, virtualization is just that: make-believe and vocabulary is part of that.

i think the O.P is actually asking how he can rename the virtualmin menus so that they show as Domain and Sub Domain (ie customise virtualmin itself)