
It probably wasn't called Deuteronomy (
Second Law). Tradition is that name was given to it by the LXX translators.
If we accept that it was the same book found in the days of Josiah, then it was just called "the book of the Law," as in 2Kings 22.
There are several theories of how the Pentateuch came to be, but many people (including me!) believe that Deuteronomy was Moses original composition, and the earliest part of the Law.
If by 'moral law' you are referring to the 10 commandments, then I agree that they all still apply. Most of them are re-stated in the New Testament anyway.