I've seen a few books called 'Beauty and the Beast' or something similar, so this is a bit of a guess. If you mean the classic fairy tale, the core trio is Belle (or Beauty), the Beast, and the enchantress who cursed him. The dad who picks the rose is pretty crucial for kicking the plot off, too.
But if it's a specific novel, like Robin McKinley's 'Beauty' or one of the modern retellings, the characters get more depth. In McKinley's version, Beauty's sisters aren't mean caricatures; they're actually supportive, which changes the family dynamic completely. The Beast is more melancholy and his library is way more impressive, which honestly is the dream.
Sometimes Gaston-type characters show up as a rival, but it's the quiet moments between Beauty and the Beast that really define the story for me. The key is always that shift from fear to understanding, which hinges entirely on those two characters.