Harry's personality could shift towards being more introspective. He would constantly be thinking about the implications of being a Riddle. His sense of justice might still be strong, but he could be more cautious in his actions. Draco might experience a major change. He might lose some of his arrogance as he realizes that being a Riddle doesn't automatically mean power and privilege. Instead, it comes with a lot of baggage. He could become more collaborative, working with Harry instead of against him, and might even show more kindness towards those he previously looked down upon.
For Harry, his normally bold and straightforward personality could become more nuanced. He may develop a sense of mystery as he delves into the secrets of the Riddle family. His relationships with his friends could also be affected. He might be more withdrawn at times as he tries to protect them from the potential danger associated with his new identity. Draco would likely see a huge transformation. His Slytherin cunning could be redirected. Instead of using it for self - gain or to put others down, he could use it to help Harry and himself navigate the complex world of being related to Voldemort. His cold exterior might soften as he discovers the importance of having a true ally in Harry.