No, the domain doesn’t have to be public. But you should put some thought into your naming strategy. Some questions to ask yourself are: Do I need more than one domain or more than one level of domains? For example, microsoft.com versus accounting.microsoft.com which adds sub domains under the main domain name. How will your web server be named and will it have a public site or intranet. Sorry to involve more questions, but for a simple, single domain, yes name it whatever you want as long as it follows MS active directory naming rules.