Paul tells his father that he's worried he's not good enough to be the future of House Atreides. Leto reassures him that regardless of whether Paul is able to step up as a leader, he will still be Leto's beloved son, and that's all that matters.
The interactions between Paul and Duncan, including one with a Bear Hug, implying Duncan was like a Cool Uncle to him. Which makes the loss of Duncan all the more tragic for poor Paul.
More in general, the interactions between Paul and other members of the House Atreides, like when arriving on Arrakis, Paul forfeits any etiquette to run to Tufir and hug him. You can see that beyond the ranks and grades, they are family to him first and foremost.