Before we get into this...
Q1. What do they call it when you have your tonsils removed?
A1. A tonsillectomy.
Q2. What do they call it when you have your appendix removed?
A2. An appendectomy.
Q3. What do they call it when a growth is removed from the top of your head?
A3. A haircut!
Now then, seriously...
Question: What do they call it when a woman undergoes cosmetic surgery to alter her labia minora (inner labia) and the labia majora (outer labia), the folds of skin surrounding her vulva?
Answer: A labiaplasty (aka labioplasty or labial reduction).
Rather than show the real thing, we have modestly used a visual metaphor to show the result of a successful labial reduction, which is to change the look of the patient's external genitalia from that on the left to that on the right.
The question Walt cannot answer is why a woman would do this. In the past five to ten years, the greatest growth in the specialty cosmetic field has been labiaplasty. It's become trendy among young white women, especially teens.
The procedure [Isn't that the word the wimmin use for "abortion"? Ed.] has some roots as a medically necessary operation. It is sometimes done to help women who experience pain because of friction caused by unusually large labia. But a significant number of those having it done have no underlying condition. Apparently they wish to alter the appearance of their genitals because they believe they do not fall within a normal range, or... just to look better.
Cosmetic surgeons argue labiaplasty can help women build confidence and resolve problems with sexual dysfunction. Critics say the desire to get labia changed is driven by unattainable standards set by the prolific porn industry [Aha! Ed.] and there is little evidence to support any claims the procedures provide women with any benefit.
Seems to me that some interesting cultural questions underlie this debate. There has been much controversy of late over genital mutilation. See, for example, "MI doctor charged with female genital mutilation; guess which religion?", WWW 17/4/17. Genital mutilation, aka "female circumcision", is a "barbaric cultural practice" (the "progressives" tell us) prevalent in the Muslim parts of Africa. In its extreme forms it can involve clitoridectomy [when they remove the woman's... never mind... Ed.]. But in less severe forms it's the trimming of the labia -- a labiaplasty.
Innocent question: If it's OK for insecure or simply vain white Western women to have labiaplasties, why is it wrong for religious brown/black Muslim women to their genitals "mutilated"? Just askin'....