All of them are the same person.

Isn't Claire unrelated somehow?

No, she's the first form Shannon's Beatrice had.

Oh, they're one yet many

I thought Clair was just a piece created by Bernkastel used to represent Beatrice.

Correct, Claire is like an understudy; she reads the lines but she isn't the real thing. She exists to conceal the appearance of the unseen "Yasu," the baby Natsuhi rejected and the original seed personality from which literally more than half the cast was born.