Mr. Farraday is a crazy-rich American who buys Darlington Hall after Lord Darlington kicks the bucket. He is decidedly less formal than Darlington, and his attempts to "banter" with Stevens throw Stevens for a loop:
It is curious how people can build such warmth among themselves so swiftly. […] But, then, I rather fancy it has more to do with this skill of bantering. (8.85)
Friendly and generous, Farraday seems to represent the ascendancy of American political and economic power after World War II, along with the relatively informal and democratic character of American society. He also represents a tidbit of hope for stuffy ol' Stevens: if Stevens can learn how to banter, maybe he can also learn how to "build warmth" around him in the form of friends.