The notation $O(X)$ seems to be a quite standard notation for the algebra of all holomorphic functions on some connected domain in $\mathbb{C}^n$ (or a complex manifold). I would like to know where did this notation come from.

John P. D'Angelo's book, simply says "See [GR, p.2] for a discussion of the etymology of this standard notation." where [GR] is Grauert and Remmert's "Coherent analytic sheaves". However I have no access to that book.