I am working on a payment form. What is that 3-digit code on the back of the card called? I can't find a consistent reference as to what to call it.
It is called the Card Security Code (CSC) according to Wikipedia, but has also been known as other things, such as the Card Verification Value (CVV) or Card Verfication Code (CVC).
The second code, and the most cited, is CVV2 or CVC2. This CSC (also known as a CCID or Credit Card ID) is often asked for by merchants for them to secure "card not present" transactions occurring over the Internet, by mail, fax or over the phone. In many countries in Western Europe, due to increased attempts at card fraud, it is now mandatory to provide this code when the cardholder is not present in person.
Because this seems to be known by multiple names, and its name doesn't seem to be printed on the card itself, you'll probably (unfortunately) still need to tell your users how to find the code - ie by describing it as the "3 digit code on back of card".
2018 update
The situation has not improved, and is now worse - there are even more different names now. However, you can if you like use different terms depending on the card type:
Note that some American Express and Discover cards use a 4-digit code on the front of the card. See the above linked Wikipedia article for more.