>>4312791technically speaking, "evangerion shin gekijōban" is the real name while "rebuild of evangelion" is just a localized one
like how the actual name of the original series is "shinseiki evangerion", meaning "gospel of the new century"
I'm not actually sure where "neon genesis" came from
maybe they though it sounded cool like with the term evangelion itself, or perharps they intended for it to be interpreted as greek for "gospel of the new beginning"
another curious language disparity is that the term used in japanese to refer to the angels (shito) is actually more accurately translated as apostle, like in berserk