Photosystem II is named as such since it is discovered after photosystem I. Their names do not represent the electron flow as it begins in photosystem II I (i.e. when both of them are present in the organism, e.g plants and algae). When photosystem II releases an excited electron, it returns to its ground state by accepting an electron from the oxidation of water molecule whereas photosystem I receives its electron from the electron transport chain, which in turn received an electron from photosystem II.
Compare: photosystem I
See also: P680