Though an undine, in folklore, was a water spirit, Undine Spragg was named, indirectly, for the French word ondule, meaning "to wave" or "to undulate". The word was from the name of a patent hair curler invented by the baby Undine's grandfather around the time of her birth. So, Undine's name is the combination of American commercialism, a mythical being, and a French word for "wave." These many layers of meaning enlighten the reader to Undine's character.
An undine was a water spirit who could gain a soul if married to a mortal man. Undine, while certainly human, lacks the "soul" of many of the people around her because she is unconcerned about anyone else's feelings. Her behavior at times becomes sociopathic, such as when she feels little to no guilt when her husband Ralph Marvell actually kills himself to save her the trouble of divorce. Undine goes from man to man, with no thought for the well-being of her son. Similarly, even when Undine's parents are experiencing a loss of income she presses them not to reduce her allowance; Undine's needs always come first. But unlike the undines of fairy stories, Undine never seems to gain a soul. At the end of the novel, when she is back with her first husband she still has no concern for him or for her child. Undine gains nothing emotionally from being with four different men during the course of novel.
The fact that Undine, the product of a Midwestern commercial family, is named after a patent hair-product is an example of Wharton's wry humor. For an American family like the Spraggs, something that would bring in the almighty dollar would be something fit to name a child after. Though er beginnings were humble, Undine shows, at various times in the novel, the ability to make good financial decisions. She is a thoroughly modern (for her time) American woman -- unlike many ladies of her social set, she was able and willing to think about money and ways to get it. That she does it unscrupulously (by marrying successively richer men) is part of her character and the product of the strictures on her sex at this time, but it is a thoroughly American, no-nonsense way of thinking about money.
That the product for which Undine was named was for women's vanity, too, is not lost on Wharton. Undine is allowed to charge through New York and, later, European society mostly because she is surpassingly beautiful. Women of lesser beauty or physical charm would either not be able to perpetuate such marital frauds (as Undine does upon Ralph and Raymond) or be allowed such collosal selfishness. Her beauty seems to give her a free pass to act as she pleases. It is a commentary on the society of this time (the "custom of the country" of the title) that beautiful young women, who do not actually incite real scandal, are not held accountable for their actions. Since Undine was, in her circle, by far the most beautiful woman, she was allowed a great latitude of behavior.
Finally, a wave seems a strange thing to equate with Undine's character. It seems to be passive, and shaped by the tide, the wind, and the shape of the shore it breaks upon. But waves are forces of nature, and they cannot be stopped. Undine lives her life like that -- pushing on toward her own goals, and sweeping everyone in her path aside. She has the mindless push of water and disregard of others that makes the wave metaphor apt.