^ I believe it's the Italian word, it was used by Honda as the Japanese name a motorbike known in the US as Honda CHF50 which Ayumi endorsed.
I'm guessing that Ayu liked the word enough to name her dog, Crea, after it. She adopted it as a pseudonym as she felt Crea was the dog that looked most like her.
Her mum is probably referring to Ayu's dog.