Maybe f it were written out with furigana as しん (shi-n) in the Japanese version. You could romanize it a couple of ways for localization; including the potentially clever sin/shin wordplay.

However, that portion of the form's name is written out with the 真 (shin) kanji. Said kanji, like all others, automatically comes with it's own distinct definition; in this case meaning true, real, genuine or even pure.

So changing it from Shin to Sin in this situation is an intentional localization alteration rather than a pronunciation issue. It may only be a one letter difference, but the change completely ignores the intended meaning in the Japanese text. If they were going for accuracy, then "真デビルトリガー/shin debiru torigā" should definitely become something like True Devil Trigger, or one of the other adjectives from the definition above. At least, unless there were furigana to indicate an alternate reading. But there are none.