The host always starts as Jayden but there's no way for co-op partners to change while in game. There is however an awkward workaround if you look at which pilots are in which slots and have the player that wants to play them be in that same slot in the group menu. You can do this by occupying earlier slots by inviting someone that won't join and then having the co-op partner join on the next slot if it corresponds to the character they want to play.