Naruto would be more impulsive. Harley doesn't really think things through, and Naruto would probably follow her lead in that regard. He might act on his emotions more quickly without considering the consequences as much. However, he'd also be more resilient in the face of setbacks. Harley has been through a lot and always bounces back, and Naruto would learn that from her.
He'd be more brash. Harley's bold and in - your - face nature would rub off on him. He'd probably be less hesitant to take risks.
His personality might become more refined. Instead of being the rowdy Naruto we know, he could be more composed and polite due to the influence of the daimyo's court.
His personality might be more reserved. Tsunade is not as boisterous as some of Naruto's other mentors. So he could be less likely to jump into things without thinking. For instance, he might analyze a situation more carefully before acting.
His sense of loyalty might change. While Naruto is fiercely loyal to his friends and village in the original story, being raised by Catwoman could make him more loyal to a smaller, more select group. He might also be more cautious about who he gives his loyalty to, as Catwoman is often on her own and has to be careful about who she trusts.
Well, it would be a really wild and crazy story. Naruto's ninja world and Harley Quinn's chaotic Gotham-esque world would collide. Naruto might pick up some of Harley's unpredictability and her sense of humor. He could also learn some unique combat styles from her. Maybe he'd be more carefree and less bound by the traditional ninja rules.
He might be more calm. Since the female Kurama could be a stable influence, Naruto wouldn't be as impulsive.
His personality would likely be more subdued. Ebisu is a rather proper and disciplined character, so Naruto would probably be less rambunctious.
His personality would likely be more reserved. Manda is not a very expressive or warm - hearted being, so Naruto might not be as outgoing as in the original story. He'd be more cautious and calculating, having learned from Manda's survival instincts.
Naruto's personality would change a great deal. He'd be less naive. Pein has seen a lot of the dark side of the world, and raising Naruto would expose him to that. So Naruto would be more world - weary. He may also be more ruthless in achieving his goals, as Pein doesn't shy away from extreme measures.
Naruto might be more assertive. Since Kushina was a strong - willed person, Naruto would likely inherit some of that. He would be less likely to be pushed around and more likely to stand up for himself earlier. Also, he might be more family - oriented as he would have grown up with a loving mother figure in Kushina.