Practice this on a Test system before attempting the Production System as this is a dangerous process. I am also presuming that you are running a fairly standard Windchill installation.
If you are running 9.1 M040 or later then just follow the ReHost Guide on the PTC website as you can rename including domain name at this release or later.
If running a previous version to this then you can follow the ReHost Guide but do not rename the JNDI repositories for LDAP and EnterpriseLDAP (if you use it). You will also need to have a host alias in your host file so that Windchill can still resolve the old hostname as well as the new hostname to the same IP.
If you have trouble accessing the principal administrator tool after the ReHost, you may need to create a new repository in the Task Delegate Administrator tool with the same config as the existing repositories.
I miss-understood you and thought that you wanted to change the hostname of your windchill installation.
Changing the Internet Domain of your Org using the Principal Administrator tool should be fine as I this is informational only.