My ideal companion would be a female player character who is a battler and whose goal is the destruction of the evil team. Maybe in this region, the evil team has wormed its way into the region's Pokémon League, or maybe the Pokémon League is the evil team, itself. The girl would have been kidnapped by the evil team when she was younger but managed to escape. Her backstory would be reminiscent of Green/Blue's (female) from the Pokémon Adventures/Special manga. It would provide a unique goal and one that could bring her into conflict with Ash, or maybe one of Ash's other traveling companions since I'd have her methods be far harsher than Ash's and the evil team would not look to be so bad at first. It would only be revealed to be really bad if one did a deep dive into the team and its background and how far it's wormed its way into decent society in the region.
She would view any gym or League challenge as a means to the end of getting rid of the evil team or at least greatly diminishing its influence on the region. This goal could also cause her to at least dabble in other things like Contests, Showcases, Pokéthelon, etcetera in order to help her develop skills that she could use against the evil team.
At the end of the region, she would join the International Police Force and become Looker's protege. Also, Looker would also help her and the rest of the group take down the evil team beforehand as well.