You use the expression, "MessiYah," and I have not found the history of that usage, though I've searched. The Hebrew word, MashiYaCH, ends in a Yod-Chet, not a Yod-Heh, thus seeming to nullify the idea that Mashiyach ends with the name of Yah.
ANSWER:
We understand that the original Hebrew does not end in "Yah". However, the original Hebrew doesn't end in the English spelling "ah" either (as in, "Messiah"). The reason we've chosen to sometimes spell it "MessiYah" is not because we believe that was the original Hebrew (anymore than "Messiah" is the original Hebrew). We just believe that YAHshua is a part of YAHweh, and as such, we like to spell it MessiYAH to make the point that we believe in their oneness.
For more articles on YAHweh's and YAHshua's oneness, CLICK HERE and scroll down to "Yahshua As Yahweh".