When must full aircraft registration be used as radio callsign?
The AIM discusses communications with ATC in Chapter 4.


  4−2−3. Contact Procedures a. Initial Contact.
  1. The terms initial contact or initial callup means the first radio call you make to a given facility or the first call to a different
  controller or FSS specialist within a facility. Use the following
  format:
  
  (a) Name of the facility being called; (b) Your full aircraft
  identification as filed in the flight plan or as discussed in
  paragraph 4−2−4, Aircraft Call Signs; (c) When operating on an airport
  surface, state your position. (d) The type of message to follow or
  your request if it is short; and (e) The word “Over” if required.
  
  c. Subsequent Contacts and Responses to Callup from a Ground Facility.
  Use the same format as used for the initial contact except you should
  state your message or request with the callup in one transmission.
  
  4−2−4. Aircraft Call Signs
  2. ATC specialists may initiate abbreviated call signs of other aircraft by using the prefix and the last three digits/letters of the
  aircraft identification after communications are established.…The pilot may use the abbreviated call sign in subsequent contacts with the ATC specialist.


When operating at a non-towered field, many pilots have begun to identify their aircraft by type and color. I’m not sure when this started, but if you listen to popular YouTube flyers like steveo1kinevo, you will notice that when they are flying into non-towered fields, they just give the aircraft type, e.g. Caravan or TBM. From a practical standpoint, it makes a lot of sense. You can’t see the numbers but you can see the type and color. And unless there are lots of white Cessnas in the pattern, it is easy to keep track of who is where. What you want to know in the pattern is where are the other planes and how fast are they going. 

Type and color gives you the necessary information. For me at least, it is easier to keep track of type and color than it is to keep track of N numbers.