The official term is hangers on from my new Codex, and there's a pretty good chance the devs heard of this because one thing that they were able to say was they've been in close contact with GW, so for theorycrafting there's a decent chance they'll take cues from the current edition of TT.
Yes I do think this is a good tie in to gang rating, lore wise it makes perfect sense, when your gang gets big and strong people will want to basically latch onto you for protection, once things are looking bad they'll soon abandon you. I really much prefer the idea of being able to rise and fall, and having upgrades tied to locations and people is a great way to do that in a way that's immersive and makes sense.
It also makes for thematic "quests" like the OP asks, that part I agree with. It becomes a little difficult again to speculate on what it should be, but assuming Settlements will be a key mechanic say to get discounts for gear sales a quest would basically be earn the favor of a settlement, maybe you rescue a trader being held hostage then you gain a hanger on who gives a flat bonus, or if Settlements offer bounties on troublemakers then collect one then that Settlement gives you a better deal. Then you can also lose it if the trader dies or get's scared off, or you lose the Settlements favor somehow. There could also be achievement quests like Mordhiem with bonuses that are more permanent, some things can be tied to the Gang as a whole, or even individual gangers.