Myrtle is an inferior version of Gatsby. Like Gatsby, she has pretensions and ambition. In the New York apartment scene that occurs in Chapter 2, Myrtle passes off a compliment about her dress--"an elaborate afternoon dress of cream colored chiffon which gave out a continual rustle as she swept about the room"-- with "It's just a crazy old thing. I just slip it on when I don't care what I look like." She later confesses that she thinks her own husband is not "fit to lick my shoe" because he borrowed the suit that he wore for their wedding. Like Gatsby, Myrtle is a social climber. She thinks she married beneath her and that Tom is the ticket to wealth and status. In her apartment in New York City, she pretends that she and Tom are in the same social class.
We learn that Tom is never going to marry Myrtle, that having a mistress in New York is akin to having horses in the stable, another form of amusement. Tom "elaborately" lies to Myrtle that Daisy's Catholic and therefore won't grant him a divorce. When Myrtle repeats Daisy's name, Tom breaks her nose. He has almost no respect for Myrtle, and only slightly more for his wife.
We should see strong parallels here between Myrtle and Gatsby. Myrtle thinks Tom will complete her dreams; Gatsby thinks Daisy will complete his. Both are sadly mistaken. Neither Tom nor Daisy will marry someone whose social class is below theirs. As Nick tells us, Tom and Daisy are "careless people." "They smashed up things and creatures and then retreated back into their money and their vast carelessness or whatever it was that kept them together, and let other people clean up the mess."
Tom smashes Myrtle's nose at the party. Daisy runs over Myrtle later on in the novel. Tom and Daisy are indeed careless people who make messes for others to clean up.
I will start with Myrtle. Once in New York, she demands to get to buy a puppy. Tom obliges and this demonstrates Myrtle's use of him. She would like to be in an upper class society and she's not. Having an affair with Tom, a man who knows no end to his money, she can spend it left and right without a care. After he buys the dog and they take it back to the apartment she changes into one of her nicer dresses. This further illustrates her desire for great things. She is a materialistic woman.
Myrtle also mocks Tom for his relationship with his wife. At first, I thought this demonstrated great courage, but I think the truth is that it shows great disrespect. She knows he is unsatisfied in his relationship with his wife and she works to rub it in.
Tom gives a tip to the man they buy the dog from ten times higher than the purchase price. This illustrates Tom's flippant attitude about money. He knows he has it and can use it.
They both believe their marriages were accidents but understand they are stuck because of Daisy's Catholic heritage that prevents divorce.