Rose Belmont is not her father. Rose is something new: the next generation of the legendary vampire hunters spending her life trying to step out of Trevor's shadow, to be seen as the self-reliant woman she is. Any monster that faces her is surprised to see a young girl, not the grizzled old man they've grown used to. But, despite these expectations, despite the long shadow her family tree casts, Rose tries to prove herself. She will not rely on, or be saved by, what came before. She will blossom into something all her own. This is her story, not his.
Castlevania: Belmont's Curse is, similarly, something new, learning from its predecessors. The first entry in the series in over a decade, and developed not internally by Konami but by the indie studios responsible for roguelike Dead Cells (including its Castlevania-themed DLC), Evil Empire and Motion Twin, it manages to stand on its own as a modern interpretation of a classic series. That said, it's far from a perfect evolution. And, just to get this out of the way: yes, it feels a little like Dead Cells in its movement, and no, since there has been some confusion online, it's not a roguelike.