It's apparent that, because of Naruto Uzumaki's duty as the Seventh Hokage, he is receiving little attention from his father, and has pushed his feelings out in mischievous schemes, much like pre-shippuuden Naruto. It is currently unknown of what his goals are, if any, or any relationships he has with the other children in his academy. He does seem to have a friendly relationship with Shikadai Nara.
He is teammates with Sarada Uchiha and led by Konohamaru, and much to her chagrin, Boruto doesn't seem to care about the status of Hokage, or even the Chuunin Exams. He's quick to give up, as evident by his resolve to use cheap jutsu-creation mechanics, rather than hard work. He is currently looking to be trained under Sasuke Uchiha.