Piggy doesn't take names in chapter 2 because of a lack of organization and authority on the island.
In chapter 1, Piggy mentions that knowing the names of the boys stranded on the island would be a good idea. This task therefore becomes his responsibility, though he struggles to remember all their names. When the island catches on fire in chapter 2, it suddenly becomes apparent that the task was never really finalized. Ralph steps toward Piggy, insisting that it was Piggy's job to "get a list of names."
Indignant, Piggy retorts that the task was impossible from the start. The little 'uns in particular are difficult to keep up with; when Piggy tried to formulate a list of their names, they refused to remain in one place long enough for him to finish the task. Instead, they rushed off to the sea or scampered into the forest. Piggy couldn't keep up with them because they constantly "scattered everywhere."
Ralph takes a moment before questioning Piggy about the implication of this assessment. He then questions whether Piggy even knows how many boys were together on the island before the fire. Piggy admits that he does not but doesn't take complete responsibility for this lack of knowledge:
How could I with them little 'uns running round like insects? Then when you three came back, as soon as you said make a fire, they all ran away, and I never had a chance ...
As the fire increases in intensity, Piggy realizes that one of the little 'uns is missing, but no one even knows the child's name.