Describe the process of working with an external domain name ?

If it is not possible for you to configure your internal domain as a subdomain of your external domain, use a stand-alone internal domain. This way, your internal and external domain names are unrelated. For example, an organization that uses the domain name contoso.com for their external namespace uses the name corp.internal for their internal namespace.

The advantage to this approach is that it provides you with a unique internal domain name. The disadvantage is that this configuration requires you to manage two separate namespaces. Also, using a stand-alone internal domain that is unrelated to your external domain might create confusion for users because the namespaces do not reflect a relationship between resources within and outside of your network.

In addition, you might have to register two DNS names with an Internet name authority if you want to make the internal domain publicly accessible.