We know nothing about this man. We meet a man with the same name in Nehemiah 3:30. Perhaps this is the same person. But, both Meshullam and Berechiah were common Jewish names, and if a person repaired a second section, that fact is (sometimes) explicitly stated (Nehemiah 3:11, Nehemiah 3:19–27, Nehemiah 3:24, Nehemiah 3:27, Nehemiah 3:30).
4 And next to them Meremoth the son of Uriah, son of Hakkoz repaired. And next to them Meshullam the son of Berechiah, son of Meshezabel repaired. And next to them Zadok the son of Baana repaired.