I always thought it was the best explicit proof of Jesus claiming the divine I AM WHO I AM from Exodus, but this made me doubt a little. Why didn't he include "ho on" like he did on the book of Revelation?
There are three different appellations in Exodus 3:14-15:
"Ehyeh-Asher-Ehyeh", variously translated as "I am that I am", "I am who I am", "I will be what I will be": And God said to Moses, "Ehyeh-Asher-Ehyeh" (Exodus 3:14a, JPS Tanakh), or I AM THAT I AM (KJV) ...
"Ehyeh", translated as "I am" or "I will be": He continued, "Thus shall you say to the Israelites, 'Ehyeh sent me to you'" (Exodus 3:14b, JPS Tanakh), or I AM hath sent me unto you (KJV)
"YHVH": And God said further to Moses, "Thus shall you speak to the Israelites: The LORD, the God of your fathers ... has sent me to you (Exodus 3:15, JPS Tanakh)
The Greek Septuagint, which is the version of the Old Testament which the New Testament generally follows, renders these three names as:
Ehyeh-Asher-Ehyeh: Ἐγώ εἰμι ὁ ὤν
Ehyeh: Ἐγώ εἰμι
Thus either ego eimi ho on or ego eimi would have been recognized as the Divine Name in Greek. We see this in John 18:4-6, as well as the passage you cite:
"Whom seek ye?" They answered Him, "Jesus the Nazaraean." Jesus saith to them, "I am" [Ἐγώ εἰμι] ... Then when He said to them, "I am," they went backward and fell to the ground
Almost every English translation of this passage inserts the word "he" after "I am", but it is actually not in the Greek text (the above translation is from The Orthodox New Testament). The Greek is accurately translating what would have been an utterance of the Divine Name, Ehyeh, by Jesus.
In this context the action expressed by the Greek verb ei·miʹ started “before Abraham came into existence” and was still in progress. It is therefore properly translated “I have been” rather than “I am,” and a number of ancient and modern translations use wording similar to “I have been.” In fact, at Joh 14:9, the same form of the Greek verb ei·miʹ is used to render Jesus’ words: “Even after I have been with you men for such a long time, Philip, have you not come to know me?” Most translations use a similar wording, showing that depending on context there is no valid grammatical objection to rendering ei·miʹ as “have been.” (Other examples of rendering a present tense Greek verb using a present perfect tense verb are found at Lu 2:48; 13:7; 15:29; Joh 1:9; 5:6; 15:27; Ac 15:21; 2Co 12:19; 1Jo 3:8.) Also, Jesus’ reasoning recorded at Joh 8:54, 55 shows that he was not trying to portray himself as being the same person as his Father.