Sammy Davis Junior, Junior is Grandpa's Seeing Eye bitch, which is "not only for blind people but for people who pine for the negative of loneliness" (1.10). So, she's basically Grandpa's companion. We get it. A dog is man's best friend and all that.
Unfortunately, she's not a very good BFF. She chews her own tail, constantly tries to hump Jonathan, and farts. Constantly. Plus she eats the map that tells them where Trachimbrod is. Despite all this, Alex says that "Sammy Davis, Junior, Junior is a very distinguished character, one with variegated appetites and seats of passion" (9.13). Okay, so we have no clue what that means, but we're glad Alex doesn't remove her from the book: every story of rape and genocide really is better with some comic relief.
But she's not just funny; she's actually kind of a foil to Jonathan. Think about it: both ride in the backseat, both are stubborn about changing their ways, and both chew on themselves: "The hero masticated the nails of his fingers, and the bitch masticated her tail" (15.8).
Thinking of Sammy Davis, Junior, Junior as Jonathan's foil makes his attitude toward her more complicated. Jonathan hates that Sammy Davis, Junior, Junior exists, and often tries to convince Alex to just excise her from the story. Are we supposed to think that maybe Jonathan doesn't belong in the story? That he's just a bumbling, masticating, farting creature who's distracting us from the real plot?