Why did Xiaoxiang Academy get this name?

It may be because:

Xiaoxiang: In A Dream of Red Mansions, Lin Daiyu is called "Princess Xiaoxiang" in the poetry society, and Lin Daiyu loves to cry, and Xiaoxiang also refers to water, so "Xiaoxiang" is often used as a synonym for Lin Daiyu in literary works. Xiaoxiang Academy is mostly romantic novels, and romantic novels often make people cry. But also because most of them read for women.