A Look at the Hebrew
Exodus 3:14 (WLC)
ויאמר אלהים אל־משה אהיה אשר אהיה ויאמר כה תאמר לבני ישראל אהיה שלחני אליכם׃
And God said to Moses: "I am who am." And he said: "Thus shall you say to the children of Israel: 'I am has sent me to you.'"
First, the word in Hebrew for 'I' (אני) can be used for direct identification: 'I am Jared' would be 'I [אני] Jared.' But in Hebrew the 'am' (ie. the being verb) is only implied in this case—there is no word for 'I am' outside the word used here (אהיה—i.e. the first person form of 'to be'), which is a form of the verb 'to be.' God doesn't use an implied being verb here because the point isn't that He exists, period, which could be said or claimed of any 'gods,' but rather than He is in an eternal present, eternally existent—the one who 'am' without reference to time altogether, with emphasis, rather, on the verb 'to be,' hence its explicit usage. That's why 'I am' in being verb form serves to identify Him uniquely to the Israelites. Using אני would not only be mysterious as 'I am' is, but meaningless: it would leave those told His name (if it were אני): You are who?? Not so with אהיה .אהיה stands alone as a statement of identity as the one who is eternally: "אשר אהיה" (the one who am being) would be redundant if it weren't for its usefulness as an expression of the uniqueness of the one Who Is (the use of אשר serves a similar function to a definite article ה here, but has more emphasis on the being verb which follows).
A Look at the Greek
Exodus 3:14 (LXX)
καὶ εἶπεν ὁ θεὸς πρὸς Μωυσῆν ἐγώ εἰμι ὁ ὤν καὶ εἶπεν οὕτως ἐρεῖς τοῖς υἱοῖς Ισραηλ ὁ ὢν ἀπέσταλκέν με πρὸς ὑμᾶς
And God said to Moses: "I am the [one] being."1 And he said: "Thus shall you say to the children of Israel: 'He who is1 has sent me to you.'"
The Greek translation in the Septuagint actually helps us understand that the Hebrew should be taken in that sense which one suspects when they see the not-commonly-used-in-similar-contexts אשר ('the one,' 'who,' 'that,' etc.) in this specific context: namely, to understand the words אהיה אשר אהיה in the sense, 'I am that unique one who can say of himself, I am.' In essence God is actually saying in Hebrew: I am the [only one who can say] I am [in the sense that it means being in both the present and eternal sense].'
The Greek translation is exactly what we would expect the Greek equivalent to be, and shows the 'I am [currently] the only being one' sense is understood in the Hebrew, giving the uniqueness of the identification (since ὁ ὤν is actually a third person reference to a unique identity which only God can fulfill in this context).
Aquila's and other possibly quite polemical, imprudently hyper-literal translations actually obscure and violate the Hebrew sense of the words. εσομαι (I shall be) is contrary to the context in which the word is used: אהיה, if not taken to mean an ongoing present existence (i.e. if taken to mean 'I shall be') would make God be promising He's going to be what He is claiming to be, which is not assurance of His identity at all—the whole intention of saying what He said! If God used the so-called perfect tense of the verb to be, He couldn't convey what He is trying to convey by the unique divine identity. He would just 'have been.' Or 'was.'
Jesus and 'I am'
As you have seen God summarized His statement 'I am [the one] who am' by saying that the take away is 'I am.' This is the part that He is actually saying is His name (the present tense 'I am being' intending to convey 'I am [who] exists eternally.' As such, The Greek εγω ειμι (I am) means exactly the same thing (or rather can be meant exactly the same way) as the imperfect tense in Hebrew used in Exodus 3:14 (which does not always mean future tense).
Understand that the Septuagint takes liberty with the translation in that it makes God use a third person identification when saying, "tell them I'm 'the One who is.'" Whereas the Hebrew uses the first person: "Tell them I'm [The One] who am." As such if Jesus were to use the equivalent of what God said in Hebrew, we would expect to see just the εγω ειμι (I am) of the Greek of Exodus 3:14 (without delving into alleged instances of such a usage).
It's my humble opinion that the Name of God in Hebrew יהוה simply means "he [who] is" (i.e. as in 'the Being One'). This is concordant with the very next verse after Exodus 3:14:
Exodus 3:15 (WLC)
ויאמר עוד אלהים אל־משה כה־תאמר אל־בני ישראל יהוה אלהי אבתיכם אלהי אברהם אלהי יצחק ואלהי יעקב שלחני אליכם זה־שמי לעלם וזה זכרי לדר דר׃
And God said to Moses again, "You shall speak thus to the children of Israel: 'Yahweh [He who is], God of your fathers—God of Abraham, God of Isaac, God of Jacob—has sent me to you.' This is my name forever: this is how I shall be known from generation to generation."
"I will be-there howsoever I will be-there" is not a translation of this Hebrew phrase (to put it as charitably as possible).
Disclaimer: I have no formal education in Hebrew or Greek. I absorb language in my own studies of the original languages in an informal way, and my explanations are somewhat anecdotal or colloquial. That said, I welcome correction.
1 When a person identifies as ὁ ὤν (the being one), i.e. uses it of themselves, it is still technically a 'third person' reference with which they are directly identifying—hence the explicit third person phrasing in the second usage of ὁ ὤν here in my translation.