Mountains Made of Glass by Scarlett St. Clair

Could you love me?" he whispered. The question stole my breath and burned my lungs in the silence that followed. 
I wanted to answer, to whisper yes into the space between us, but I was afraid.
All Gesela's life, her home village of Elk has been cursed. And it isn't a single curse - it is one after another, each to be broken by a villager, each with devastating consequences. When Elk'swell goes dry, it is Gesela's turn to save her town by killing the toad that lives at the bottom. Except. . .the toad is not a toad at all. He is an Elven prince under a curse of his own, and upon his death, his brothers come for Gesela, seeking retribution.
As punishment, the princes banish Gesela to live with their seventh brother, the one they call the beast. Gesela expects to be the prisoner of a hideous monster, but the beast turns out to be exquisitely beautiful, and ratherthan lock her in a cell, he offers Gesela a deal. If she can guess his true name in seven days, she can go free.
Gesela agrees, but there is a hidden catch - she must speak his name with love in order to free him, too.
But can either of them learn to love in time?