First off, it's hard to think of a more appropriate title for this story than "The Storm." There would be no story without the storm; it guides the entire narrative and affects each of the characters in some way. It's almost more the storm's story than the characters'.
Since the story wasn't published until after Chopin died, we can be pretty sure that she named the story without input from an editor or publisher (source). This story is all hers, and so is the title.
On a deeper level, the title refers to more than just the meteorological storm; it may also allude to Calixta and Alcée's explosive and life-changing sex. For more on the idea of the storm as a symbol, check out our section, "Symbolism, Imagery, Allegory: The Storm."
By the way, it's worth noting that the story originally had a subtitle, too: "A Sequel to 'At the 'Cadian Ball" (source). Chopin's story "At the 'Cadian Ball," which takes place years before "The Storm." Want to know what happens in that story? Of course you do:
Bobinôt wants to go to a ball because Calixta might be there. He likes her, but she doesn't seem to like him back. Meanwhile, Alcée has fallen for Clarisse, who doesn't seem to like him back either. The night of the ball, Alcée decides to cope with his poor harvest by drinking and heading to the dance, even though he's from a different class than Bobinôt and Calixta and seems somewhat out of place there. (See "Setting" for more on class differences in the story.) At the dance, Alcée and Calixta separate from everyone else, and we find out that he's involved in a romantic scandal from her past. They seem to still have feelings for each other. Suddenly, Clarisse shows up and makes Alcée go away with her. Calixta is left behind and asks Bobinôt to take her home. As they're leaving, she accepts his proposal of marriage. Meanwhile, Clarisse confesses that she loves Alcée as the ball ends.