To esteem something means to value it and to delight in it (Isaiah 13:17), to regard something highly, and to have great respect for it. In this case, those who esteem the name of the Lord are put in contrast to the faithless in Israel who have lost all respect for the Lord because of his failure to respond as they expected by rewarding them for their good works or punishing the wicked for their evil works.
16 Then those who feared the LORD spoke with one another. The LORD paid attention and heard them, and a book of remembrance was written before him of those who feared the LORD and esteemed his name.