In my textbook Analysis I by Amann/Escher, there is Remark 3.7 about inner product space as follows:
From this Wikipedia's page, the definition of Hermitian function is given as:
We have $\overline{(x|y)} = (y|x)$ and $(y|x)$ is not necessarily equal to $(-x|-y)$. As such, I think the inner product is not necessarily Hermitian w.r.t Wikipedia's definition.
Could you please confirm whether my understanding is correct or not?