Which of the king's eunuchs did Esther send to find out why Mordecai was mourning in sackcloth?

Answer: Hathach

Esther sent Hathach, a eunuch appointed to her. Mordecai gave him a copy of Haman's decree to show her, urging her to plead with the king.

“Then Esther summoned Hathach, one of the king’s eunuchs appointed to her, and she dispatched him to Mordecai to learn what was troubling him and why.”— Esther 4:5 (BSB)