Changing A Child's Surname

The situation is this. One of my nephews was born out of wedlock. And to make it safe for the child, they decided to take the mother's sister and her husband parents.but child, now that the child is already 15 years old, she asked to have the name his father is his surname too. And the biological father is also willing to give his name to the child. I want to ask if this can be done and how it start witha

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