Windows Server 2003 to 2012 & Domain Rename

Hi Team,

There seems to be a lot of outdated information on the web regarding domain names.
Currently my environment is running Windows Server 2003, we're looking at upgrading to 2012 (on a completely new server) and possibly rename our domain from internal.name.com (for security reasons I'll blank the name) to internal.newname.com.

Can someone please point me in the right direction for help with this?
We do not run MS Exchange locally, we run Office 365 which runs separately and we do not have it linked to AD for single sign-on yet.