Which eunuch had charge of the young women and advised Esther before she went to the king?

Answer: Hegai

Hegai, custodian of the women, favored Esther, and she asked for nothing except what Hegai advised.

“When the king’s command and edict had been proclaimed, many young women gathered at the citadel of Susa under the care of Hegai. Esther was also taken to the palace and placed under the care of Hegai, the custodian of the women.”— Esther 2:8 (BSB)