I've had to watch some explanatory videos to understand the Mandalorian lore. And one thing that was mentioned is that the person who tames a Mythasaur is traditionally the leader, the Dark Saber only came along much later. So it may be that Bo-Katan rides the Mythasaur and becomes the leader based on that alone. The other options would be Din Jaren wielding the saber and them leading together, or they may just have battle it out.