John Gill Commentary Ezra 2:61

"And of the children of the priests: the children of Habaiah, the children of Hakkoz, the children of Barzillai, who took a wife of the daughters of Barzillai the Gileadite, and was called after their name." — Ezra 2:61 (ASV)

And of the children of the priests Who could not make out their pedigree, for those that could are mentioned before:

the children of Habaiah, the children of Koz, the children of Barzillai ; how the latter came by this name follows:

which took a wife of the daughters of Barzillai the Gileadite, and was called after their name ; this man married a woman that descended from the famous Barzillai the Gileadite, in the times of David; and the priesthood being in disuse, and mean and despicable, in Babylon, he chose to take the name of his wife's family, and pass for a descendant from that, and perhaps destroyed, or at least neglected, to take care of the genealogy of his own family.