Body piercings (and other modifications) tend to have two or more names. The first is almost always based on the anatomy itself, and in the cases of the "basics" may be the only name in common use (ie. Navel Piercing, Nipple Piercing, and so on). In addition to the anatomical name, many piercings often have a "descriptive" or "proper" name as well, this name being chosen by a piercer or client to perform/receive the piercing while it has no known name (ie. "Scrumper" or "Smiley" versus "Upper Lip Frenulum Piercing"). Some piercings such as the Madison are known almost exclusively by their proper name.
Because until recently there has been no true mass media servicing the piercing community, this practice has lead to many piercings having numerous local terms that are unknown outside of the city (and sometimes even studio) they originated in.
If you want to name a new piercing (first take a look around BME to see if someone already has — very few piercings are truly "new" at this point), the key is publication — and when you do publish it, be sure that the name is included! Many piercings are in common circulation without a name until someone decides to apply one in public.