Yes, except the Old Testament God doesn't say "I am who I am" but "I will be who I will become."
That still doesn't address my question. :)
Ehyeh-Asher-Ehyeh.
The Incommunicable Name was pronounced "Adonai," and where Adonai and Yhwh occur together the latter was pronounced "Elohim." After the destruction of the Second Temple there remained no trace of knowledge as to the pronunciation of the Name (see Jehovah). The commentators, however, agree as to its interpretation, that it denotes the eternal and everlasting existence of God, and that it is a composition of (meaning "a Being of the Past, the Present, and the Future"). The name Ehyeh () denotes His potency in the immediate future, and is part of Yhwh. The phrase "ehyeh-asher-ehyeh" (Ex. iii. 14) is interpreted by some authorities as "I will be because I will be," using the second part as a gloss and referring to God's promise, "Certainly I will be [ehyeh] with thee" (Ex. iii. 12). Other authorities claim that the whole phrase forms one name. The Targum Onḳelos leaves the phrase untranslated and is so quoted in the Talmud (B. B. 73a). The "I AM THAT I AM" of the Authorized Version is based on this view.
Didn't Popeye say that?