Neo is "New" in Greek. New in Japanese is "Shin" (新). When writing English words in Japanese katakana, there's no distinction between "s" and "sh" sounds.
Presumably this dude used 新 at first and then the English letters/katakana for "Sin," but since that doesn't translate well the translators used "Neo" instead. That's just a guess though; I haven't seen the raws.
Thanks @Remlpsum, that makes some sense. (Though later on the Neo was never mentioned again..) I had totally forgotten about the meaning of "shin" as well. 😅
He definitely gave himself the nickname Man of Sin. I bet he was workshopping his name while deciding whether to wear a regular or a torn up cloak, other ideas he had we Dark Emperor Supreme and Flame Lord Noir.