John 17:11-12:
"I am no longer going to be in the world; and yet they themselves are in the world, and I am coming to You. Holy Father, keep them in Your name, the name which You have given Me, so that they may be one just as We are. While I was with them, I was keeping them in Your name, which You have given Me; and I guarded them"
What is this Name?
For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace. [Isaiah 9:6 KJV]
Charles John Ellicott expounds on this text and makes it clear that this is the 'name' that the Father gives to the Son.
His name shall be called Wonderful.—It is noticeable that that which follows is given not as many names, but one. Consisting as it does of eight words, of which the last six obviously fall into three couplets, it is probable that the first two should also be taken together, and that we have four elements of the compound name: (1) Wonderful-Counsellor, (2) God-the-Mighty-One, (3) Father of Eternity, (4) Prince of Peace. Each element of the Name has its special significance.
(1) The first embodies the thought of the wisdom of the future Messiah. Men should not simply praise it as they praise their fellows, but should adore and wonder at it as they wonder at the wisdom of God (Judges 13:18, where the Hebrew for the “secret” of the Authorised version is the same as that for “wonderful;” Exodus 15:11; Psalm 77:11; Psalm 78:11; Isaiah 28:29; Isaiah 29:14).
The name contains the germ afterwards developed in the picture of the wisdom of the true king in Isaiah 11:2-4. The LXX. renders the Hebrew as “the angel of great counsel,” and in the Vatican text the description ends there. (2) It is significant that the word for “God” is not Elohim, which may be used in a lower sense for those who are representatives of God, as in Exodus 7:1; Exodus 22:28, 1Samuel 28:13, but El, which is never used by Isaiah, or any other Old Testament writer, in any lower sense than that of absolute Deity, and which, we may note, had been specially brought before the prophet’s thoughts in the name Immanuel.
The name appears again as applied directly to Jehovah in Isaiah 10:21; Deuteronomy 10:17; Jeremiah 32:18; Nehemiah 9:32; Psalm 24:8; and the adjective in Isaiah 42:13. (3) In “Father of Eternity,” (LXX. Alex. and Vulg., “Father of the age to come “) we have a name which seems at first to clash with the formalised developments of Christian theology, which teach us, lest we should “confound the persons,” not to deal with the names of the Father and the Son as interchangeable. Those developments, however, were obviously not within Isaiah’s ken, and he uses the name of “Father” because none other expressed so well the true idea of loving and protecting government (Job 29:16, Isaiah 22:21).
The answer to your question can be found in Acts 4:8-12 NIV:
8 Then Peter, filled with the Holy Spirit, said to them: “Rulers and elders of the people! 9 If we are being called to account today for an act of kindness shown to a man who was lame and are being asked how he was healed, 10 then know this, you and all the people of Israel: It is by the name of Jesus Christ of Nazareth, whom you crucified but whom God raised from the dead, that this man stands before you healed. 11 Jesus is
“‘the stone you builders rejected, which has become the cornerstone.’[a]
12 Salvation is found in no one else, for there is no other name under heaven given to mankind by which we must be saved” (the bolding is mine).
I find the following excerpt from https://www.gotquestions.org/meaning-name-Jesus.html to be particularly helpful regarding Jesus's name:
The name Jesus, announced to Joseph and Mary through the angels (Matthew 1:21; Luke 1:31), means “Yahweh saves” or “Yahweh is salvation.” Transliterated from Hebrew and Aramaic, the name is Yeshua. This word is a combination of Ya, an abbreviation for Yahweh, the name of Israel’s God (Exodus 3:14); and the verb yasha, meaning “rescue,” “deliver,” or “save.”
The English spelling of the Hebrew Yeshua is Joshua. But when translated from Hebrew into Koine Greek, the original language of the New Testament, the name Yeshua becomes Iēsous. In English, Iēsous becomes Jesus. Thus, Yeshua and, correspondingly, Joshua and Jesus mean “Yahweh saves” or “the Lord is salvation.”
The name Jesus was quite popular in first-century Judea. For this reason, our Lord was often called “Jesus of Nazareth,” distinguishing Him by His childhood home, the town of Nazareth in Galilee (Matthew 21:11; Mark 1:24; Luke 18:37; John 1:45; John 19:19; Acts 2:22). Despite its commonness, the name Jesus is remarkably significant. Jesus was sent by God for a particular purpose, and His personal name bears witness to that mission. Just as the Yeshua/Joshua in the Old Testament led his people to victory over the Canaanites, the Yeshua/Jesus in the New Testament led His people to victory over sin and their spiritual enemies.
The primary reason Jesus in his high priestly prayer asked his Father to protect the people the Father had given to him and to keep them in that name, is because that name meant salvation for them and for all of God's chosen ones who were to come to faith in the succeeding generations.
The unity that believers from all generations can and should experience and demonstrate is made possible by the saving power of the name of Jesus. In other words, the "holy catholic (or universal) church" is and forever shall be one in Jesus. That unity supersedes all the man-made labels that tend to separate Christians worldwide, such as nationality, language, color, socio-economic status, and of course denominations!
11 I will remain in the world no longer, but they are still in the world, and I am coming to you. Holy Father, protect them by the power of [Or, Father keep them faithful to] your name, the name you gave me, so that they may be one as we are one (John 17:11 NIV).
A suggestion offered by the New American Bible Revised Edition is that the text refers to "I AM." This is the name YHWH used when he first identified himself to Moses at the Burning Bush:
13 Moses to God, “if I go to the Israelites and say to them, ‘The God of your ancestors has sent me to you,’ and they ask me, ‘What is his name?’ what do I tell them?” 14 God replied to Moses: "I am who I am." Then he added: This is what you will tell the Israelites: I AM has sent me to you."
In addition, John's gospel uses the phrase I AM several times to emphasize either God's eternal being itself or Jesus' unity with the Father. (Jn 8:24, 28, 58; 13:19)
I conclude that the most likely name indicated here is "I AM."
Addendum: It may also be that Jesus refers to God's traditionally unutterable name (YHWH), which God allowed him to both know and pronounce. Also, he might have in mind biblical prophecies such as
What is the meaning of the words:”your own name, which you have given me”?
The name “Jesus”corresponds to the Hebrew name Jeshua (or, in fuller form, Jehoshua), meaning “Jehovah Is Salvation.”
Accordingly, twice in this chapter Jesus emphasizes that he made the name Jehovah known. (Joh 17:6, 26)
In the Bible, the term “name” may also stand for the person himself, his reputation, his qualities, and all that he declares himself to be. (on Mt 6:9; Joh 17:6.)
So besides bearing a name that incorporates the divine name, there were apparently other ways that the name Jehovah has been given to Jesus.
For example, Jesus reflected perfectly the personality of his Father. (Joh 14:9) Also, Jesus came in his Father’s name and performed powerful works in that name.—Joh 5:43; 10:25.
Excerpt taken from this JW publication
In John 17:11 “Father” can be understood to be the referent of “Your name.”
Holy Father, keep them in Your name. - NASB
In addition to the other answers and to other names that one may think of, the one that stands out in chapter 17 of John is “Father.” The name “Father” is given to Jesus as one who alone can properly address God as Father (cf Jn 3:16). But it is also given to him in the sense of one who is the exact representation of the Father (cf Jn 14:9-10, Heb 1:3).
It appears five times in Jesus’ prayer (vv. 1, 5, 11, 21, 25). Notably, in verses 11 and 25, it is modified by the adjectives holy (v11) and righteous (v25) respectively. “Father,” when modified thus, is a formal way of addressing God and not just an expression of their personal relationship and intimacy.
In context “Father” is the name that is most consonant with the carefully laid out themes of unity, protection and love in John 17. Perhaps more than any other, it reflects the character of God as seen in Jesus’ person and teaching. It is, I believe, the love of God as Father that Jesus invokes when he prays for us to be kept in his name.
Ellicott's commentary on Jn 3:16
God wills not that Abraham should give his son, but He gave His only begotten Son. The dread power that man has ever conceived—that is not God; the pursuing vengeance that sin has ever imagined—that is not God; the unsatisfied anger that sacrifice has ever suggested—that is not God. But all that human thought has ever gathered of tenderness, forgiveness, love, in the relation of father to only child—all this is, in the faintness of an earth-drawn picture, an approach to the true idea of God.
