You are referring to Exodus 3:14. The majority of scholars believe that the name Yahweh predates the compilation of the Book of Exodus (Shemoth) and that the "He is I am" etymology is an after-the-fact explanation referred to as a re-etymologization.
Re-etymologization is a common occurence in the ancient world. To give just a couple of examples, the Black Sea was originally known to the Greeks as Axeinos, "the Inhospitable", not because it was difficult to navigate, but because it most closely approximated the Old Persian akhshaina ("dark blue" or "black" ). When they had colonized the entire littoral of the Black Sea, they changed its name to Euxeinos, or "the welcoming". Similarly, Jerusalem ("City of Peace" in Hebrew) was re-etymologized into Greek as "Hierosolyma" because "hiero-" designated that it was the "holy" city.
The designation of the Jews as "the people of Yahweh" goes back at least to the 13th Century B.C. Current scholarly opinion is that the Torah was not compiled until much later, but in no event any earlier than the reign of Solomon. If you are interested in just WHY this opinion is held, I would recommend two excellent books on the subject, both by Richard Elliott Friedman, the first entitled "Who Wrote the Bible?" and the second "The Hidden Book in the Bible".
I'm not sure if that clarifies things in terms of why I dismissed the "He is I am" etymology, but I hope so.
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