Going by the above, it must be stated that in Modern Hebrew the word for religion in relation to a "god" based faith is (דת) pronouced "Dawth or Dat." Though the word (דת) is derived from the ancient, Mishnaic, etc. Hebrew word (דת), the word in more ancient forms of Hebrew does not mean "religion" at all and does not relate to the faith in a deity at all. The below describes how the word, at least in ancient Yehudi / Yisraeli cultures the word would be better translated into English.
Thus, there is no word in Ancient Hebrew to denote what is modernly meant by the word "religion" and thus in Modern Hebrew the word in Ancient Hebrew of (דת), as a part of the evolution of Hebrew as a language in the national setting.
Taking this into account, the word in Modern Hebrew for Judaism is (יהדות). The Modern Hebrew word (יהדות) is derived from an older group of Hebrew words of either (דת יהודית) "Dath Yehudith" meaning the
"customs, laws, practices, ec. of the Yehudim (Judeans/Jews)" or from the later term (יהדות), due to the evolution of the langauge, came to mean the same thing.
That being said, at the time of the terms being spoken of the people in question who used the term the
"customs, laws, practices, ec. of the Yehudim (Judeans/Jews)" was the Torah that they claimed was given to their ancestors as a part of a mass revelation at Mount Sinai, but the Source of creation/reality/etc. which I will use the term Hashem to describe. I.e. when I use the term Hashem, I am using it to describe the Source of creation/reality/etc. not as I or anyone else beleive it to be - but instead as it is in reality whether we know that reality or not.
Support for what I mentioned comes from the following sources of Jewish history. Mishnah Mesecheth Kevuvoth 7 Mishnah 6, Talmud Bavli Mesecheth Ketuvoth 92, and others.
Also, according to the Academy of the Hebrew Language, here in Israel, the above information is supported. It describes both the source and the root of the word (יהדות) "Yahaduth" as I described above. Even in modern Hebrew, the definition of the word, by way of etymology, is not related to the modern concept of a religion, but instead
"customs, laws, practices, ec. of the Yehudim (Judeans/Jews)".