I'm not entirely keen on the idea of a game score per se, but a journal that better tracks aspects of your adventure like total renown and infamy with various groups you've met and why, such as listing quest goals completed that favor them and crimes against them could be interesting.
The question that always comes up is how much the player should know. Like should you just automatically know how various groups feel about you, or should you have to talk to any member or a specific noble whose tracking that and can tell you the populaces' feelings regarding you. And while the game obviously tracks a lot of things numerically, should that info be displayed numerically or with general verbal terms. It's not like df civs have a social credit score system like China uses, so they wouldn't be tracked like a number by even the nobles who would be keeping tabs on you. Should they post a bounty/reward system, like you committed X crimes but performed Y services or deeds that helped their cause, so they'll forgive your criminal bounties and offer you 500 units currency. But such a bounty system might prove too gamey too, and some crimes like murder might not be forgivable by paying a bounty depending on civ ethics. And every civ has different ethics, so crimes are considered differently.
A numerical value of the total sum of coins you're carrying would be nice. Different civs use different currencies so it's hard to get an idea how much money you're actually hauling around just talking to one guy at a time.