I am Turkish and I think I didn't understand your question quite well. A lot of Turkish people has 2 names, yes. But it is not different than having only 1 name. One is free to use either of them, or sometimes both together. Why would be using one of a person's names haram?
Names are determined by parents. Sometimes mother & father want different names for a child (usually grandparents would involve naming issue), and usually they put both of them. The child can use either of them, or both of them. Some people switch between their names if they have another friend with a single name which is same with their mostly used name in order to avoid collision.
Also some parents want to give some historical/famous names for their children like Mehmet Ali, Mehmet Emin, Ali Bahadır, etc.