In theory, the realm name is arbitrary. You can call your realm whatever you
want.

However, in practice a Kerberos realm is named by uppercasing the DNS domain
name associated with the hosts in the to-be named realm. In other words, if
your hosts are all in the foo.org domain, you might call your Kerberos realm
FOO.ORG.

If you wish to have more than one Kerberos realm associated with the same
DNS domain name, the convention is to create realms that are in the same
hierarchy of your DNS domain name. For example, if you wish to have two
Kerberos realms in the DNS domain foo.org for Human Resources and Sales, you
might create the Kerberos realms HR.FOO.ORG and SALES.FOO.ORG.

The convention to use uppercase for realms names arose out of the desire to
easily distinguish between DNS domain names (which are actually
case-insensitive) and Kerberos realms. The Kerberos realm name is case
sensitive (the realm foo.org is different than the realm FOO.ORG). You are
not required to have an uppercase Kerberos realm, but I would strongly
advise it.

It is worth noting that the recent revisions to the Kerberos standard have
specified that uppercase realm names are preferred and lowercase realm names
have been depreciated.