The name Bentham is a possible reference to Jeremy Bentham, an influential British philosopher who advocated the principles of utilitarianism. According to the philosophy of utilitarianism, the rightness of an action must be judged by the consequences of the action. Thus, any action that provides the greatest pleasure to the greatest number of people can be considered a "good" action. Jeremy Bentham hypothesized that morally righteous actions result from the desire to avoid pain and the need to achieve pleasure.
This utilitarian theory is quite clearly seen in the story. Jackson does not tell us why there is a need for the lottery, merely that it is deemed necessary to the community in question. Thus, one unfortunate person is sacrificed annually in order to produce the greatest happiness for the greatest number of people in the community. However, the question begs to be asked: can any amount of collective happiness justify the cold execution of an innocent? Perhaps the main reason Jackson does not provide a rationale for the lottery is to illustrate the dangers of such thinking.
Another name in the story, Martin, may be a reference to Martin Luther, the originator of the Protestant Reformation in the 16th century. Martin Luther's teachings about sanctification and his exposure of internal ecclesiastical corruption became highly popular with congregations in England. Eventually, armed with the teachings of Martin Luther and John Calvin as inspiration, Puritans (those who believed in purifying the church from within) made their way to New England. In the 1630s, almost 20,000 Puritans set sail for New England. Yet, in their fervent desire to purify the church, Puritans often became intransigent in spiritual matters.
To illustrate the dangers of such intransigence, it is noteworthy that Jackson includes the name Hutchinson in the story. The name is quite possibly a reference to Anne Hutchinson, a New England religious leader who settled in the Massachusetts Bay Colony in 1634. As a leader, Anne advocated a different approach to personal salvation: she posited that good works alone could not lead to salvation. Resolutely, she stressed the importance of an individual's personal religious experience over the ecclesiastical authority of the minister's. This led to conflict within the colony and eventually caused Anne to be excommunicated from the Church of Boston. Thus, it is fitting that, in Jackson's story, Tessie Hutchinson is the one chosen for execution. Like Anne before her, Tessie is rejected and disposed of by the community.