I don't see the point in saying my call sign at all. Who even takes note of the other call signs, other than the type of plane if someone is announcing? I just hear "Springfield traffic Cessna blahblahblah turning base for 18 springfield". Then I'm looking for a cessna. It just wastes time saying your call sign.
At Compton, just over from Long Beach, at any given time there may have been 15 152s in the pattern between 25L&R. Too short of a call doesn't cut it, you need call signs and you need to understand who is in front, behind, and opposite you in the pattern.