If I were named in the tradition of the Iraqi people, my name would be Emily Larry John. While helping my Iraqi friend fill out paperwork, I noticed that his last name was different from his wife's, and that the children had an entirely different last name. Each person is given a first name. The middle name is his/her father's name, and the surname is the paternal grandfather's name. Each person actually has many, many names which are basically a list of the paternal ancestors. Upon marriage, the wife does not take the husband's name but keeps the names of her father and grandfather.
Imagine having the same middle and last names as your siblings for your entire life. Or, imagine your children having no name in common with you if you're a female. Instead your children are identified by your husband and male in-laws. In our American society it would get even trickier. Divorce is so prevalent; there are also many children that don't know the identity of their father, especially when a single woman decides to adopt or conceive by in-vitro. I guess it works in their society because everything is so much more traditional. And, a person's family of origin is very important.