Reputation System For Player Made Factions

I have created an ai faction to learn how to make a reputation system for factions. I then made it so players can form and join factions and recruit npc to join their faction and do various jobs. But I want to add a reputation system to the player made factions however normally I would use a dedicated variable but the faction names are player persistent variables and therefore infinite. There are infinite formable factions so I cannot exactly make a dedicated variable for every faction. So how do I solve this? I tried a discord server but no one there could help me!