The name Muley Graves is a great example of a charactonym. A charactonym is a character's name which implies something distinctive about the character. In the Harry Potter books, for example, Draco Malfoy is charactonym because draco means dragon (in Latin), mal means bad (as in malpractice) and foy is an old English word broadly meaning loyalties. So Draco Malfoy's name translates as dragon of bad loyalties, which seems rather apt.
The name Muley most obviously suggests 'like a mule,' and so has connotations of characteristics associated with that animal, namely stubbornness and hardiness. The character Muley Graves in the story is certainly very hardy. He lives a tough, difficult life on the land, and he is most definitely stubborn, refusing to leave his land or his house after the bank evicts his family.
The surname Graves also fits the character very well. In chapter 6, Muley says of himself that he is "jus' wanderin' aroun' like a damn ol' graveyard ghos'." This refers to how empty and desolate the land is now that his "folks all went away out west." The land has also, in a sense, been left to die, and Muley wanders aimlessly like a ghost, feeling as if the life he has now is like death compared to what there was before.
Mules are notoriously stubborn (hence the word "mulish"), and to be grave is to be serious. Graves are also directly related to death, so the name suggests someone who is stubborn, seriously so, perhaps stubborn to the point of death.