New Domain Name

I’m setting up a new company domain. I’ve registered a domain name online (let’s say mycompany.com). I have a web site online (let’s say www.mycompany.com) that is currently hosted for us. I have several other web sites (let’s say www.employeesonly.mycompany com, www.webmail.mycompany.com, etc.) that I host myself on our internal servers. We’re setting up a new corporate office, new servers, new everything. I have the opportunity to set this up right. I’ve heard that it’s best NOT to name your windows domain the same as your public domian (so not mycompany.com). Is this true? What are the standard naming conventions for a windows domain? Any tips for doing this right would be helpful.
Thanks,
Sean