Behindthename.com gives, as the site you found did, ‘Hodel’ as a diminutive of Hode, but goes on to say that Hode is the shortened form of Hadassah.
Hadassah is the Jewish name of Queen Esther. The site goes on to relate:
The Book of Esther in the Old Testament tells the story of Queen Esther, the Jewish wife of the king of Persia. The king's advisor Haman persuaded the king to exterminate all the Jews in the realm. Warned of this plot by her cousin Mordecai, Esther revealed her Jewish ancestry and convinced the king to execute Haman instead.
Wikipedia gives a little more detail:
Esther is described in all versions of the Book of Esther as the Jewish queen of a Persian king Ahasuerus. In the narrative, Ahasuerus seeks a new wife after his queen, Vashti, refuses to obey him, and Esther is chosen for her beauty. The king's chief adviser, Haman, is offended by Esther's cousin and guardian, Mordecai, and gets permission from the king to have all the Jews in the kingdom killed. Esther foils the plan, and wins permission from the king for the Jews to kill their enemies, and they do so. Her story provides a traditional background for Purim, which is celebrated on the date given in the story for when Haman's order was to go into effect, which is the same day that the Jews killed their enemies after the plan was reversed.
In the Singer story Adele renounces her Jewish ancestry in order to ensure she can be buried as she wishes.
I’ve only seen a summary of the story, so can’t comment if there are other call-backs to/inversions off the story of Esther.