First let us understand this so called name Emmanuel

Therefore the Lord Himself will give you a sign: Behold, the virgin shall conceive and bear a Son, and shall call His name Immanuel. (Isaiah 7:14 NKJV)

Now upon closer examination of the Hebrew you will see that this name Emmanuel comes from two words.

עמנו אל

The First Word
Uses the Hebrew letters (Ayin - Mem - Nun - Vav), these letters represented through English characters (Omnu).

This word gets translated as "with us"

The Second Word
Uses the Hebrew letters (Aleph - Lamed), these letters represented through English characters (Al)

Al gets translated as God
with us God

If Jesus was Emmanuel why was Christ named Yeshua?
He wasn't named "Yeshua". Yeshua is so a translation attempt however it cannot be correct. The English Y stems from a Hebrew Vav not the Hebrew Yud.

The Prophet was to come in his Name

I will raise up for them a Prophet like you from among their brethren, and will put My words in His mouth, and He shall speak to them all that I command Him. 19 And it shall be that whoever will not hear My words, which He speaks in My name, I will require it of him.

It was foretold that a virgin shall give birth and the new born will be named Emmanuel then why was Jesus named "Yeshua". Please explain...
The poorly translated word Emmanuel means "With us God". The Father's name is so composed from the four Hebrew letters Yud Hey Vav Hey. However simplified often to two letters Yud Hey. Now to get the correct pronunciation we can refer to the rules of Hebrew pronunciation and the example given to use by the Greek usage of the name of Jesus.

The Beginning I to Iesou the Greek rendition of the holy name represents the Yud. Another way to pronounce a Yud is so yodh. The Greek Iota is so the same letter. That's how we got the English I. The letter J transformed from the letter I during the 1800s. It got its J sound through French influence in romantic dialect.

The Greek Epsilon represents the Hebrew Hey. Therefore the Je in the beginning of the name of Jesus actually represents the holy name for God. However in pronunciation the Greek ie can carry the sound of the letter i for the word "in".

The next Greek letter the sigma sounds like an S.

In Hebrew form of the name of Jesus the final letter is so the Ayin, a silent letter. So the name of the "I am" is so also "Is".

Also the holy name we find both with the aleph prefix and also the Yud prefix. So in most cases where it is so translated as Lord would mean "he am" not "I am" therefore more appropriate to English and the holy name "Be", for it also says Holy "Be" thy name, "he Is". - it is what it is, it will be what it will be, I am that I am. Amen (so Be it).

Let me use verses from Old Testament and New Testament:

Isaiah 7:14 (NIV) - Therefore the Lord himself will give you a sign: The virgin will conceive and give birth to a son, and will call him Immanuel.

Matthew 1:23 (NIV) - “The virgin will conceive and give birth to a son, and they will call him Immanuel” (which means “God with us”).

In Aramaic, it must be noted that Immanuel is written as "Ammanueil" (Aramaic form of Hebrew name "Immanuel").

In Matthew 1:25, we see the naming of the child which is "Yeshua" in Aramaic (in English "Jesus").

I believe Aramaic name "Yeshua" can mean "YA has equated." YA (in Aramaic OT and Aramaic NT) is the Aramaic form of Hebrew "YH" in "YHWH." Because of this, Hebrew name "Yehochanan" is "Yochanan" in Aramaic. Another example is Hebrew name "Yehonathan" is "Yonathan" in Aramaic. For Respect, "YA" is addressed as "MarYA" (Master YA) in Aramaic OT and Aramaic NT.

From what I learned, YA has equated (Yeshua) the mankind by becoming a human being. Through this, God is with us.

John 1:1 (NIV) In the beginning was the Word, and the Word was with God, and the Word was God.

John 1:14 (NIV) The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth.

Jesus Christ is the Word of God, who himself is God, who became flesh and made his dwelling among us, hence, the meaning, "God with us".

Isaiah 7:14 (NIV) Therefore the Lord himself will give you a sign: The virgin will conceive and give birth to a son, and will call him Immanuel.

Matthew 1:23 (NIV) “The virgin will conceive and give birth to a son, and they will call him Immanuel”(which means “God with us”).

Notice here that Isaiah simply gave the name but Matthew gave us the meaning of the name Immanuel as "God with us". Isaiah also gave other names for the Messiah.

Isaiah 9:6 (NIV) For to us a child is born, to us a son is given, and the government will be on his shoulders. And he will be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace.

Since Immanuel was not the only name predicted by Isaiah, it has to do with the attributes of the Messiah. Literally, Jesus Christ is the meaning of Immanuel, God who dwelled among us, who became human, hence the title "Son of Man".

Matthew 26:63-64 (NIV) But Jesus remained silent. The high priest said to him, “I charge you under oath by the living God: Tell us if you are the Messiah, the Son of God.” “You have said so,” Jesus replied. “But I say to all of you: From now on you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven.”

His whole title in Aramaic is actually " ישוע משחא בר אלהא אחדאיא ", or "Jesus the Messiah, the only Begotten Son of God", according to the Nicene creed written in Aramaic. It shows how God is with us in that respect.

Not only that, but the prophecies in Isaiah can be taken to mean qualities of the Messiah, literally being called (qarat shemo וְקָרָ֥את שְׁמ֖וֹ, or in Aramaic taqarai shemieh תקרי שמיה ), as in He will be called Immanuel, otherwise, it would have been "at shimo את שמו".

Also in this verse, the literal Hebrew and Aramaic both state that his name will be called, not that his name will be.

Isaiah 7:10

Therefore the Lord himself will give you a sign: The virgin will conceive and give birth to a son, and will call him Immanuel.

• לָ֠כֵן יִתֵּ֨ן אֲדֹנָ֥י ה֛וּא לָכֶ֖ם א֑וֹת הִנֵּ֣ה הָעַלְמָ֗ה הָרָה֙ וְיֹלֶ֣דֶת בֵּ֔ן וְקָרָ֥את שְׁמ֖וֹ עִמָּ֥נוּ אֵֽל

It's not directly "at shimo Immanual" it's "qarat shimo", or "called the name Emmanuel".

The Aramaic Targum and Hebrew text out the prophecy, showing it's what earlier Jews believed. It is as much a name as it is a title of Christ.

For a further understanding on how that works, look at Gen 17:19.

Genesis 17:19

Then God said, "Yes, but your wife Sarah will bear you a son, and you will call him Isaac. I will establish my covenant with him as an ever lasting covenant for his descendants after him.

• וַיֹּ֣אמֶר אֱלֹהִ֗ים אֲבָל֙ שָׂרָ֣ה אִשְׁתְּךָ֗ יֹלֶ֤דֶת לְךָ֙ בֵּ֔ן וְקָרָ֥אתָ אֶת־שְׁמֹ֖ו יִצְחָ֑ק וַהֲקִמֹתִ֨י אֶת־בְּרִיתִ֥י אִתֹּ֛ו לִבְרִ֥ית עֹולָ֖ם לְזַרְעֹ֥ו אַחֲרָֽיו׃

With the naming of Issac (Yitzhak). "w qarat at-shimo yitzkhaq וְקָרָ֥אתָ אֶת־ שְׁמ֖וֹ יִצְחָ֑ק". The accusative is here to show that his name will be indeed Yitzkhak, while in Isaiah, the prophecy states that "qarat shimo Imanuel", no "at" at all (no pun intended).

This "at" particle, according to An Introduction to Biblical Hebrew Syntax By Bruce K. Waltke, Michael Patrick, it states on page 162, section 10.1

...the particle at is often used with the definite accusative

In this case, with Yitzkhak, it's definite because it's saying his (the name) will be Issac. In Jesus' case, the name Imanuel does not directly refer to his name actual, but something he will be called. The same thing in Isaiah 9:6, there is no 'at' particle to show that it would be his actual name.

Isaiah 9:6

For to us a child is born, to us a son is given, and the government will be on his shoulders. And he will be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace.

-כִּי־יֶ֣לֶד יֻלַּד־לָ֗נוּ בֵּ֚ן נִתַּן־לָ֔נוּ וַתְּהִ֥י הַמִּשְׂרָ֖ה עַל־שִׁכְמֹ֑ו וַיִּקְרָ֨א שְׁמֹ֜ו פֶּ֠לֶא יֹועֵץ֙ אֵ֣ל גִּבֹּ֔ור אֲבִיעַ֖ד שַׂר־שָׁלֹֽום׃

Again, we only see וַיִּקְרָ֨א שְׁמֹ֜ו, and there is no אֶת־שְׁמֹ֖ו, or the direct prophecy that his name will be, as how Issac was named.

You are confusing titles with proper names.

1. Yesh'ua (Heb.) is rendered "Jesus" or "Joshua" today. It is his given name. It means "Jehovah Saves."

2. Christos (Greek) is a title translating the Hebrew "Messiah" or "Annointed One." It highlights his annointed and special status.

3. Immanuel (Heb.) is a simple Hebrew construction that says "God is with us." It is as much sign as name. It signifies that in coming to Earth, God has chosen to dwell among us.

It would be akin to asking "Why is Obama referred to as POTUS when his parents called him Barak and his friends call him Barry?" Each title, name, and construct reveals more information about the identity of this man, or in the case of Jesus, this God who became Man and dwelt among us.