Begovic is a very 'shouty' goalkeeper, and has more experience of PL football than most in our squad (all bar perhaps Defoe). He's one who should be a leader. Steve Cook is a long time club servant and will be a mainstay of the side for the foreseeable. Lewis Cook has been captain of various youth sides down the years, he's another in time. Ake is a big presence as well as the club's best player, so he's another who should be providing leadership.
There's only so long that Francis and Surman can be the two captains, they are objectively two of the older players, and subjectively two of the weaker players, in the core squad. There are others who need to be stepping up, or should be allowed the freedom to step up.