Old Deerfoot is a crucial middle man in the Lees' story. Without Mr. Deerfoot, the Lees would not have met up with the Company for the Feast of Pure Brightness to restore good will between the men. Without Old Deerfoot, Miss Whitlaw would have no way of contacting the Company to find out what is going on with Moon Shadow's cryptic phone call in Chapter 12. And we all know that if Miss Whitlaw hadn't contacted the Company, then the Company wouldn't have come help the Lees in Oakland, and then Dragonwings would never have flown and the book would have a majorly different effect. So, thanks, Old Deerfoot, for being a totally useful minor character.
Old Deerfoot's name gives us some clue to his function as a supporting character, too. That was an attempt at a pun: get it? Foot, support? We might expect Old Deerfoot to be the gentle man of peace that he is given that he's named for a gentle animal. Plus we know that Old Deerfoot is a man that minds his etiquette. After all, Moon Shadow remarks on his politeness in sitting for tea for half an hour before getting to the matter at hand (9.10).