It's Baathist culture.

Your name in Baathist culture is [your first name] [your father's name] [your grandfather's name].

So her name is Raghad Saddam Hussein because her father's name is Saddam and her grandfather's name is Hussein.

Hussein is actually Saddam's middle name, named after his father. His real last name is Abdul Majid, which was Hussein's father's (Saddam's grandfather's) name.

This was done by Baathists to reduce tribal interference and to push their understanding of Arab nationalist identity and socialist ideology.

In a passport one would usually find three names: the name of the person, the name of their father, the name of the grandfather. However, the actual surname, which is the indication of the tribe or region one belongs to, was not written in the passport. The Iraqi government came up with this deliberate policy in order to not identify the area or tribe a person comes from for security reasons. This practice was partly a protection for the individual. If somebody is e.g. called a Tikriti, it is easy to know that they are part of the ruling family which may expose them to particular security risks.

http://www.globalsecurity.org/military/world/iraq/tribes-2.htm

When you see last names with prefixes of "al" it refers to their tribe.