My favorite interpretation is as follows:
They brought the woman to be stoned. However, the law was that BOTH the adulterous woman and adulterous man were to stoned. Yet in an effort to trap Jesus, they brought only the woman. Had he said “stone her” as required by law he would have been condemned because the law required both. However, in bringing only the woman before Jesus, the Pharisees were the ones that had sinned.
To let them know that, Jesus wrote in the sand the name of the man whom also committed adultery with the woman.
An alternative is that he wrote the names of the mistresses of the Pharisees that were present to shame them into dispersing.
Those are my favorite theories, but Jerome’s explanation fits best with its mirroring new testament with old and the fulfillment of yet another prophecy.
And it could be all of the above.
I’m pretty sure it was names though and that’s why they aren’t recorded in scripture. Because God isn’t going to record the names of those he has consigned to the dust.