Off the cuff, I'd say it goes the other way. The fame and reputation is some simple bit outside all the other mechanics, representing indirect power and influence, which your Background may very well interact with, but not drive.
For example, if you are noble, it's easier for you to lend money to other nobles (depending on the social aspects in the campaign). But getting the money in the first place is something that any adventurer can do.
Fame and reputation are like equipment. They are part of your character in one sense, but not another. There are times and places where they matter more or less, and they can change or even be lost without really changing your skills, spells, etc.