The answer to this question comes in Chapter 7, which narrates the Ceremony of the Twelve where Jonas and his friends are given their assignments. The community meets in the auditorium all together and each group sits together - not families together, but year groups together. We are not given that much information about the chief elder, except that she is female and it is her job to give the introductory speech at this important ceremony. The Chief Elder obviously has the role of being key in making the decisions about assignments, and therefore knows each of the new twelves very well. Note for example, the introduction she gives to Asher before he receives his assignment:
"When the committe began to consider Ahser's Assignment," she went on, "there were some possibilities that were immediately discarded. Some that would clearly not have been right for Asher."
She goes on to narrate amusing stories about Asher and his past misdemeanours before finally announcing his Assignment. Therefore the chief of the elders is a very important person in this society and has knowledge of every person in it.