From my experience in other games, you guys can make Trainer Card that can show ;
How many badges earned !
Win - lost rate (PvP only / NPC wins not count )
Total amound of money that player currently have (maby)
Current 6 pokemon on that players team (just picture of pokemons not special infos like pokemons LvL or stats )
How long he is playing ingame time (maby starting date too)
And the BEST of that thing is you can just add an option for players like " Show my Trainer Card" or " Hide my Trainer Card" in Trainer Card section for those who dont want to give out info. So noone can Harash / Bully people who is sensitive about it.
i definetly want to see that thing in future!