I have manifested thy name unto the men which thou gavest me out of the world: thine they were, and thou gavest them me; and they have kept thy word. (John 17:6) [KJV]
And I have declared unto them thy name, and will declare it: that the love wherewith thou hast loved me may be in them, and I in them. (John 17:27)
These are two different claims. In 17:6, Jesus states He manifested the name. Manifested is Ἐφανέρωσά which Thayers says here means to make known by teaching. In 17:27 He states He declared (ἐγνώρισα) the name unto them and will declare (γνωρίσω) it. Declare is to make known.
Certainly there are grounds to debate what "the Name" is and in what language Jesus spoke or may have spoken, and how did Jesus manifest the Father's Name. Yet if one accepts the text as written, then the point of emphasis becomes what Jesus claims He will do. That is, He is going to do something which He has already done. In terms of the Name, the prayer closes such to alert the reader to consider what is about to happen.
After praying Jesus and His disciples cross the Kidron brook and enter the garden where He is arrested. When He is confronted, John (chapter 18) records what Jesus said:
4 Jesus therefore, knowing all things that should come upon him, went forth, and said unto them, Whom seek ye?
5 They answered him, Jesus of Nazareth. Jesus saith unto them, I am he. And Judas also, which betrayed him, stood with them.
6 As soon then as he had said unto them, I am he, they went backward, and fell to the ground.
7 Then asked he them again, Whom seek ye? And they said, Jesus of Nazareth.
8 Jesus answered, I have told you that I am he: if therefore ye seek me, let these go their way:
9 That the saying might be fulfilled, which he spake, Of them which thou gavest me have I lost none.
Twice Jesus said ἐγώ εἰμί, literally, "I am" yet translated as "I am he." John records Jesus had spoken these words earlier: to the woman at the well (4:26); to those in the Temple Treasury (8:24, 28, 58); to the disciples at the Last Supper (13:19).
Apparently, from John's perspective, the name of the Father is ἐγώ εἰμί (I am) as is found in the Greek translation of the Old Testament:
13 And Moses said unto God, Behold, when I come unto the children of Israel, and shall say unto them, The God of your fathers hath sent me unto you; and they shall say to me, What is his name? what shall I say unto them?
14 And God said unto Moses, I Am That I Am: and he said, Thus shalt thou say unto the children of Israel, I Am hath sent me unto you. (Exodus 3)
και ειπεν ο θεος προς μωυσην εγω ειμι ο ων και ειπεν ουτως ερεις τοις υιοις ισραηλ ο ων απεσταλκεν με προς υμας
The expression εγω ειμι ο ων can be parsed as Father, εγω ειμι, and Son, ο ων. So the Name given to Moses is Father and Son, εγω ειμι ο ων. Then Moses was sent by the Son ο ων. John, on the other hand, records Jesus was sent by the Father, εγω ειμι.
This echoes the conclusion of the Prologue:
No man hath seen God at any time; the only begotten Son, which is in the bosom of the Father, he hath declared him.
θεὸν οὐδεὶς ἑώρακεν πώποτε μονογενὴς θεὸς ὁ ὢν εἰς τὸν κόλπον τοῦ πατρὸς ἐκεῖνος ἐξηγήσατο
No one has ever seen God; the only God, THE ONE WHO IS, has himself led out into the bosom of the Father.
1. Robert G. Hall, "The Reader as Apocalyptist", John's Gospel and Intimations of the Apocalyptic, Eds. Catrin H. Williams and Christopher Rowland, Bloomsbury Publishing, 2103, p. 268