its tough to say why he was given his mother surname?but i think as the ninetail fox was sealed inside him by his father(yondaime).,by giving the surname of his father he might know he was the jinchuriki of kyuubi. inorder to keep it secret his father gave him surname uzumaki.so that he never know about the kyuubi.
because people didnt want naruto knowing that minato was his father :| so if he was naruto namikaze, he would know that he's the fourths son.....so to hide that he was, they gave him Uzumaki....
because people didnt want naruto knowing that minato was his father :| so if he was naruto namikaze, he would know that he's the fourths son.....so to hide that he was, they gave him Uzumaki....