Angential

The pride flag for angenital - unknown color meanings, flag maker is known online as uchuulien

Angenital can be defined as someone who "feels uncomfortable (potentially dysphoric) about having any kind of genitalia". People who are angenital do not mind having gendered pronouns (she/her/hers or he/his/him for example). People who are angenital don't mind having a gender identity that is relating to the feminine spectrum (such as demigirl) or masculine spectrum (such as libramasculine). Angenital has been known to be shortened to "ANG". 

The name of the surgery to "be rid of one's own genitals" is called "gender nullification". Those who have had often report difficulty with urination post-surgery ("holding it in" as well as being more prone to infections). Different surgeons remove different amounts of body parts (depending on the specific client's wishes as well as laws regarding this type of severe body modification). Often times post surgery clients have to take some kind of supplemental hormone. 

Through the research that I did, it is not clear if this type of surgery is still considered legal in the USA (I found conflicting articles about this). Some people who have gone through with this surgery have stated that they reached out to surgeons who had experience with transgender individuals who wanted to change their genitalia. 

In regards to Facebook groups, there is not a lot out there. On Fetlife, there is one gender nullification group. 

The reason why people do this extreme body modification is generally given as "I never felt comfortable with me body in that area - I just want it gone."