[morningseagulls]

>She should use 鹄(swan) instead of 鹅(goose). Yes people don't usually use this character for swan

I've never heard of or seen this character until today.

>most people know of it as it's part of the idiom: 燕雀安知鸿鹄之志.

"Most people" usually mean "people around me", so it's not indicative.

There are plenty of ethnic Chinese people not living in China who might not have heard of this idiom -- in part because their knowledge of Chinese may not be as deep as people who've gone through the Chinese education system -- and one of them had probably advised Swanson on her name choice.