As I understand it, neutrinos were first proposed to explain energy and momentum conservation in beta decay, as a hypothetical particle emitted together with the electron and proton. Thus Pauli gave the name "neutrino" to what is now called an "anti-neutrino" in the reaction
$$n \to p^+ + e^- + \overline\nu_e$$
Apparently the renaming had to do with lepton number conservation.
Typically, the decision to classify a particle as "anti-" or "non-anti-" would I think be based on which form is most commonly observed in the real world. Do we have evidence to suggest that neutrinos are more common than anti-neutrinos? Is the question even meaningful?