New information on the clicks via an article at Wired:
Rendell and his collaborators, including biologists Hal Whitehead, Shane Gero and Tyler Schulz, have for years studied the click sequences, or codas, used by sperm whales to communicate across miles of deep ocean. In a study published last June in Marine Mammal Sciences, they described a sound-analysis technique that linked recorded codas to individual members of a whale family living in the Caribbean.The video above (not part of the study) has several minutes of clicks.
In that study, they focused on a coda made only by Caribbean sperm whales. It appears to signify group membership. In the latest study, published Feb. 10 in Animal Behavior, they analyzed a coda made by sperm whales around the world. Called 5R, it’s composed of five consecutive clicks, and superficially appears to be identical in each whale. Analyzed closely, however, variations in click timing emerge. Each of the researchers’ whales had its own personal 5R riff...
Moreover, 5R tends to be made at the beginning of each coda string as if, like old-time telegraph operators clicking out a call sign, they were identifying themselves. Said Rendell, “It may function to let the animals know which individual is vocalizing.”..
That individual whales would have means of identifying themselves does, however, make sense. Dolphins have already been shown to have individual, identifying whistles.