Good Society Tracker system
For a game I ran a while back, I used a 1-20 score for Reputation, just like a regular ability score.
That also conveniently gave a modifier that I could use in relevant rolls, and I also split the score into bands where 1-3 was hostile, 4-8 was disliked, 9-11 was neutral, 12-16 was liked and 17-20 was favoured. I used that to get a simple way to figure out how willing a faction would be to help/hinder the party, and what that help/hindrance might look like.
Changing reputation was relatively simple. A minor interaction moved reputation +/- 1 as relevant. A major interaction moved reputation +/- 1d4 in the relevant direction.
Wasn't an especially complex system, but it worked really well for my purposes as I was dealing with 9 different factions and how they interacted with the party at the time. Could easily expand it out to interfaction reputation, but I didn't find that necessary personally as the much greater focus was on the party-faction relations.
Source: https://www.reddit.com/r/DnD/comments/13dshtk/what_is_a_good_system_for_tracking_reputation/