My son has his fathers last name, but I want to add and hyphenate my maiden name with my son's last name. Do I need his fathers permission to do this? Or can I just add it on without his permission? What are the legal rights in Darwin, NT, Australia for this situation?

Here is the website of your State body government. They would be better able to advise you of your local law and regulations.

Department of Justice (http://www.nt.gov.au/justice/bdm/index.shtml)