Short Answer: Stanley is Yelnats spelled backwards.

In chapter 7, the audience learns about Stanley Yelnats's great-great-grandfather, Elya, who was cursed by Madame Zeroni after neglecting to carry her up a mountain while singing her a pig lullaby. Shortly after Elya Yelnats decides to let Igor marry the shallow, ignorant Myra Menke, he becomes a deckhand on a ship sailing to America and eventually arrives in the United States, where he falls in love with a woman named Sarah Miller. Even though Elya is cursed, Sarah agrees to marry him and they eventually have a child, whom Sarah names Stanley. Sarah came up with the name after noticing that Stanley is Yelnats spelled backward, which is what is unique about the name. The name is then passed down through generations and the protagonist of the story struggles to overcome his family's curse. Eventually, Stanley carries Zero to the top of God's thumb and sings him a pig lullaby, which breaks the longstanding family curse.