We are planning to build a new forest and multiple domains. We want to know if it is possible to have the name of the domain not inherit from the forest. For example
Domain 1: xyz.com
Domain 2: def.com
Yes and no.
The first domain in the forest is knows as the "forest root domain" and shares a name with the forest. So, in the configuration that you're describing, you'll actually need three domains. The forest root will be
Yes this is possible. You had to create a new Tree Root Domain.