Like someone else said, her name is literally a curse that binds he to basically be her older sister's slave.Speaking of her sister, how she could hijack Dara-san's body when she died years ago? Is this about the name of Dara-san literally older sis's name (kanji)? I check chapter 15 and only see her arms and legs got eaten.
It goes even deeper than that, Dara (formerly Koharu) wanted to forget her name because of what it meant, but she didnt fully get over it. She's been used, abused and conditioned to just be a tool for the older sister to do with as she pleases for all her life. Dara was still not over that mental fuckery her family did and thus ended up letting her sister take over once the name/curse got activated.
The siblings being so defiant and having had such a strong influence on Dara through their silly brand of worship tought her that its ok to be a bit selfish at times and reject stuff you dont like. Basically, they undid the mental damage her sister did and gave Dara the chance to fight back.
When Hinata says "im the older sister, its my duty to save my little brother" and offered herself to Dara without hesitation nor care for the repercussions, that showed Dara what a true big sister should be like. It was the final push that let her renounce her old name, accept her new one as "Dara" that isnt a title and fully reject the evil older sister. She fully recognized the failure the older sister is and embraced what the misogiya siblings gifted her.