When a new user to the portal is created, he receives an email with a link to confirm his account. By default, the email contains a variable ${action_url} which is the server's name (ex. https://<<SERVER_NAME>>:8443/TestDataManager/resetPassword.html). Could it be possible to change this address for our domain name (ex. https://<<DATAPORTAL_URL>> ?

Release:
Component: TDMWBP

Great news!  There is a method to customize Portal Screens.  To answer your specific question, please backup and make a copy of the file and then edit: %Portal_Home%\Program Files\CA\CA Test Data Manager Portal\Mail Templates\WelcomeEmailTemplate.vm

In the future, when you upgrade, you will need to re-customize each page changed.