[One of my players asked for some kind of game structure around reputation and notoriety. Here's my quick version of what I think I'm going to try out this week.]
Reputation exists within a certain context which we'll call a peer group. Everyone in the peer group knows the reputation of everyone else in the peer group. A minor embarrassment (by the standards of that peer group) such as not getting invited to a party costs you 5 reputation (within that peer group), while a minor victory (getting a famous celebrity to attend) earns you 5 reputation. A major embarrassment (clothes catching on fire at a party) could cost up to half your reputation or 100 points (whichever is greater), while a major victory (saving the city) could double it. (DM's discretion here as to magnitude.) The only mechanical effects of reputation are that you can give it away to someone with less reputation, you can spend it to "attack" the reputation of someone who has less than you do (degrading both equally on a 1:1 basis), and everyone knows how much reputation everyone has. The additional roleplaying consequence is that people who want reputation within a certain peer group are likely to cooperate with those with high reputation, who therefore have the power to enhance or destroy other people's reputations. Toadies and flunkies, in-groups, out-groups, etc., all emerge naturally from this simple set of rules.
You can participate in multiple peer groups and have different reputations within each. I might have loads of street cred (Reputation: 500 among the Waterdeep Toughs) but be virtually unknown amongst the nobility (Reputation: 5 for once attending a certain party) and yet be hated and feared by chromatic dragons (Reputation: 200 for killing three dragons). Note that Reputation doesn't have to mean that people like you (the dragons hate me), but if I want to spend my credibility mocking a certain chromatic dragon he has to respond (likely by trying to kill me) or be shamed among his peers. A regular peasant wouldn't have that kind of leverage.
Notoriety is reputation with a peer group of bad guys.
The point of the reputation system is so that players can know in advance, some quantifiable way, what abstract effects their actions will have and thereby increase their feeling of agency. In my specific player's case, last week he rescued some peasants from gnolls and then threatened them afterward when they failed to give him any money. He ended up destroying their house, barn, and prized plow. In the proposed system, that might be -100 reputation among People Who Live Near Adarak, and +5 among Manly Psychopaths Who Live Near Adarak. The gnolls might even be peers within the Manly Psychopath peer group, and those of them who survived undoubtedly would lose reputation (-20 reputation?) if word of their defeat got around. How that affects their behavior depends on how important their reputation is to them, and what they think is the best way of getting it back.
Finally, I might build in some quick handles into every peer group that let you gain some starting reputation. E.g. Street Toughs might give you an initial reputation equal to your Intimidation passive score, and Nobility might let you gain 5 reputation with a week's worth of effort and a successful Persuasion check against 1/5 your current reputation. The purpose of the handles is, again, to empower the players with specific knowledge about their options.
If I esteem mankind to be in error, shall I bear them down? No. I will lift them up, and in their own way too, if I cannot persuade them my way is better; and I will not seek to compel any man to believe as I do, only by the force of reasoning, for truth will cut its own way.
I could not love thee, dear, so much,
Loved I not Honor more.