Why would the Puritan townsperson reference him(Daniel) in this situation? -Chapter 3, page 60
You must be referring to this quote:
Of a truth, friend, that matter remaineth a riddle; and the Daniel who shall yet expound it is yet a-wanting."
Daniel was a prophet in the bible. Not to be confused with the David of the bible, who would have had many concubines and women. The Puritan woman who makes this sentence is essentially saying that because Hester won't talk and the magistrates cannot seem to figure out who the father is, they need a spiritual person to discern the truth and figure it out. Today we could use paternity tests. Back then, they would have heavily relied on a dream interpreter like Daniel to explain what the truth of the riddle might be. They are hoping a person will step forward to interpret the situation and reveal the truth to everyone.
Daniel of the bible was able to interpret dreams and would give even divulge consequences of the future if certain steps were not taken.
There is a reference shortly after to the guilty one, but the paragraph is not clear that Daniel and the guilty one are the same "he" referred to later.
ANOTHER INTERPRETATION could be that Daniel and the guilty one are the same person. But, this does not seem Puritan-like. To make a biblical allusion to Daniel would be to look for someone to be the master revealer. But infidelity does not align with the character of Daniel. Therefore, the reference might only be to the guilty man, whoever he is, to be a great revealer in order to tell the people he is Hester's secret lover.