Paul could be an allusion to the Paul found in the New Testament. Originally named Saul, he received a vision from God and was then blinded for three days. This vision led him to a new truth, and his life's focus took on an entirely new meaning. The Paul in this short story also receives visions while on his rocking horse, and this changes the focus of his life. He now lives to acquire money in an attempt to make his mother happy. Ultimately, he sacrifices his own life to do so. After much suffering, the Biblical Paul also died as a martyr.
Hester is Paul's mother. The name is only revealed at the very end of the story. Her name could be a nod to another famous literary Hester found in The Scarlet Letter: Hester Prynne. Hester Prynne is ostracized from her society, struggling to find friendship or acceptance because of a child conceived outside marriage. Paul's mother feels that she struggles to find acceptance in her society. She is always longing for more money to make better social connections, but never quite reaches her goal. Paul's mother isn't nearly as noble as the Hester found in The Scarlet Letter, and this contrast demonstrates the shallowness of Paul's mother.
The name Bassett conjures associations with a basset hound—a loyal, friendly, and devoted breed. Bassett serves this role to young Paul, encouraging him in the most loving ways. However, Bassett doesn't act like a rational adult in this story; he fairly blindly follows the whims of a child, making him seem more like "man's best friend" rather than a source of adult protection.