As an allegory, The Lottery was written with many purposefully symbolic elements. Like other allegories (such as The Scarlet Letter or The Pilgrim's Progress) many of the characters names are supposed to be symbolic.
Mr. Summers: despite the fact that Mr. Summers is intimately involved in the tradition of the lottery, his name suggests joy, positivity, energy. This character is symbolic of the dual nature of this town - one that can host a variety of positive activities in addition to the yearly ritual of death: "square dances, the teen club, the Halloween program, and of course, the lottery." Mr. Summers is involved in everything.
Mr. Graves: as the postmaster of the town, Mr. Graves holds a position of power. His name, Graves, suggests something ominous and/or related to death. He helps Mr. Summers carry out the procedure of the lottery directly associating the "death" connotation of his name to the lottery itself.
Old Man Warner: the "Old Man" part of this characters name suggests he is a constant in the town, someone who has been there so long, no one remembers a time when he wasn't there. Old Man Warner symbolically represents the tradition of the town and therefore the tradition of the lottery. Also, his last name, Warner, suggests him to be "One who warns."
Mr. Adams: he is the first character to draw for the lottery because Adams comes first alphabetically, but this is also a direct reference to Adam as the first man (Biblical reference). Interesting too, the Adams' are among only a few characters who question the lottery. This could be directly compared to Adam and Eve "questioning" God when they ate the fruit and changed the course of mankind forever.
Mrs. Delacroix: she is a character who is known for her inconsistency and seeming two-faced nature. Her last name literally translates in French to "of the cross" and her name could be symbollic of the same two-faced nature of the crowd in the New Testament who decided crucify Jesus Christ instead of Barrabus.
*Below you find a link to further examples of symbolism in the short story.