In Amy Tan's The Joy Luck Club, the reader learns that names are very important. They are not haphazardly chosen for a Chinese child, but are believed to reflect the true essence or nature of the person who is "carrying" the name. This information is shared in the chapter entitled, "A Pair of Tickets."
As June (Jing-Mei) advances along in her trip through China, she finds herself on a journey to discovering more about her mother, her sisters, and, most importantly—and surprisingly for her—herself.
The names of the mother and her daughters are symbolic to the story: June's mother's name meant "Forever Never Forgotten." However, as her mother chose to write the characters of her name, it meant "Long Cherished Wish," reflecting her desire to find again in June what she had lost in being separated from her twins: a daughter.
In that June's mother chooses to write her name this way, we can infer that this form of her name reflects who she became after losing her twins. And this must have been in her mind when she named June. "Jing" means the "pure essence" of something valuable (like gold) after the impurities have been removed. "Mei" is from "meimei (a common name), used to mean "younger sister." So Jing-Mei's name is to reflect the pure essence of the younger sister. Amy Tan writes:
I think about this. My mother's long-cherished wish. Me, the younger sister who was supposed to be the essence of the others.
At the same time in the story, June's father notes that her sisters' names (the twins) are Chwun Yu and Chwun Hwa, which mean (respectively): "Spring Rain" and "Spring Flower," names of "newness" (as in "spring") and beauty—rain and flower. Perhaps their mother saw that one existed for the other—they could not be complete with the other.
With the use of these names, June's mother has shared not only her perceptions of, and hopes for, her daughters, but also what was important to her—her daughters and a "long cherished wish" that they might one day be united (even though she did not know for sure that the twins had survived). She dreamed about all of them existing completely—only by being connected in some way—which occurs when June travels with her father to China, fulfilling her mother's wish.