"their given" is correct and usable in written English.
You can use it to refer to something that has been designated to a particular group of people. For example, "The students worked hard to earn their given grades."
Both girls received their given names from the sheik.
Worse, they said, it could give media companies too much political control in their given markets.
Torn from their homes, they no longer use their given names.
But often their actions contradict their given characters, and the irony doesn't always feel intentional.
Saudis use at least three names: their given name, their father's name, and their tribal name.
Each school has well-qualified faculty members who are each experts in their given fields.
Here, children named Jake and Jonquil call friends' mommies by their given names.
In captions, we learn their given kunyas, or Arabic noms de guerre.
BEIJING — Chinese women, like Chinese men, are identified by their surnames followed by their given names.
They've already established professional reputations and networks of contacts who know them by their given names.
But most famous athletes are now best known by their given name.
