It would likely make Draco more self - reflective. Discovering a twin would force him to question his own identity. He might start to see himself not just as a Malfoy heir but as an individual separate from the expectations placed on him by his family.
Draco's relationships with others would change. For instance, his relationship with his parents might become more complex as they deal with the existence of another child. And his friendships at Hogwarts, like with Crabbe and Goyle, could be affected as he spends more time trying to understand his twin.